diff --git a/src/sage/categories/category_types.py b/src/sage/categories/category_types.py
index ed4fdce2c62..faf22f2f3e3 100644
--- a/src/sage/categories/category_types.py
+++ b/src/sage/categories/category_types.py
@@ -616,8 +616,8 @@ def __contains__(self, x):
         """
         if super().__contains__(x):
             return True
-        from sage.rings.ideal import is_Ideal
-        return is_Ideal(x) and x.ring() == self.ring()
+        from sage.rings.ideal import Ideal_generic
+        return isinstance(x, Ideal_generic) and x.ring() == self.ring()
 
     def __call__(self, v):
         """
diff --git a/src/sage/combinat/finite_state_machine.py b/src/sage/combinat/finite_state_machine.py
index 480c4b4f890..b5facfc94a5 100644
--- a/src/sage/combinat/finite_state_machine.py
+++ b/src/sage/combinat/finite_state_machine.py
@@ -10790,8 +10790,8 @@ def entry(transition):
             else:
                 base_ring = transition_matrix.parent().base_ring()
                 from sage.rings.polynomial.multi_polynomial_ring \
-                    import is_MPolynomialRing
-                if is_MPolynomialRing(base_ring):
+                    import MPolynomialRing_base
+                if isinstance(base_ring, MPolynomialRing_base):
                     # if base_ring is already a multivariate polynomial
                     # ring, extend it instead of creating a univariate
                     # polynomial ring over a polynomial ring.  This
diff --git a/src/sage/crypto/lattice.py b/src/sage/crypto/lattice.py
index 513730ff89f..1078f419132 100644
--- a/src/sage/crypto/lattice.py
+++ b/src/sage/crypto/lattice.py
@@ -22,7 +22,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 
 def gen_lattice(type='modular', n=4, m=8, q=11, seed=None,
                 quotient=None, dual=False, ntl=False, lattice=False):
@@ -254,7 +254,7 @@ def gen_lattice(type='modular', n=4, m=8, q=11, seed=None,
 
         P = quotient.parent()
         # P should be a univariate polynomial ring over ZZ_q
-        if not is_PolynomialRing(P):
+        if not isinstance(P, PolynomialRing_general):
             raise TypeError("quotient should be a univariate polynomial")
         assert P.base_ring() is ZZ_q
 
diff --git a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
index 2b9dd28b13b..5229e1c9f74 100644
--- a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
@@ -46,7 +46,7 @@ class initialization directly.
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.fraction_field import FractionField
 from sage.rings.fraction_field import FractionField_generic
-from sage.rings.quotient_ring import is_QuotientRing
+from sage.rings.quotient_ring import QuotientRing_nc
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space_field
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space_finite_field
@@ -268,7 +268,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
             PR = PR.ring().change_ring(K).fraction_field()
             polys = [PR(poly) for poly in polys]
         else:
-            quotient_ring = any(is_QuotientRing(poly.parent()) for poly in polys)
+            quotient_ring = any(isinstance(poly.parent(), QuotientRing_nc) for poly in polys)
             # If any of the list entries lies in a quotient ring, we try
             # to lift all entries to a common polynomial ring.
             if quotient_ring:
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
index a04cf57a28d..a553b9dd3a8 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
@@ -94,9 +94,9 @@ class initialization directly.
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.flatten import FlatteningMorphism, UnflatteningMorphism
 from sage.rings.morphism import RingHomomorphism_im_gens
-from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.quotient_ring import QuotientRing_generic
 from sage.rings.rational_field import QQ
 from sage.rings.real_mpfr import RealField
@@ -384,7 +384,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
             polys = list(morphism_or_polys)
             if len(polys) == 1:
                 raise ValueError("list/tuple must have at least 2 polynomials")
-            test = lambda x: is_PolynomialRing(x) or is_MPolynomialRing(x)
+            test = lambda x: isinstance(x, PolynomialRing_general) or isinstance(x, MPolynomialRing_base)
             if not all(test(poly.parent()) for poly in polys):
                 try:
                     polys = [poly.lift() for poly in polys]
@@ -394,8 +394,8 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
             # homogenize!
             f = morphism_or_polys
             aff_CR = f.parent()
-            if (not is_PolynomialRing(aff_CR) and not isinstance(aff_CR, FractionField_generic)
-                and not (is_MPolynomialRing(aff_CR) and aff_CR.ngens() == 1)):
+            if (not isinstance(aff_CR, PolynomialRing_general) and not isinstance(aff_CR, FractionField_generic)
+                and not (isinstance(aff_CR, MPolynomialRing_base) and aff_CR.ngens() == 1)):
                 msg = '{} is not a single variable polynomial or rational function'
                 raise ValueError(msg.format(f))
             if isinstance(aff_CR, FractionField_generic):
@@ -3533,7 +3533,7 @@ def affine_preperiodic_model(self, m, n, return_conjugation=False):
                         if hyperplane_found:
                             break
                 else:
-                    if is_PolynomialRing(R) or is_MPolynomialRing(R) or isinstance(R, FractionField_generic):
+                    if isinstance(R, PolynomialRing_general) or isinstance(R, MPolynomialRing_base) or isinstance(R, FractionField_generic):
                         # for polynomial rings, we can get an infinite family of hyperplanes
                         # by increasing the degree
                         var = R.gen()
@@ -4598,7 +4598,7 @@ def preperiodic_points(self, m, n, **kwds):
                     for k in ZZ(n).divisors():
                         if ZZ(n/k).is_prime():
                             Sn.append(k)
-                    if (is_PolynomialRing(R) or is_MPolynomialRing(R)):
+                    if (isinstance(R, PolynomialRing_general) or isinstance(R, MPolynomialRing_base)):
                         phi = FlatteningMorphism(CR)
                         flatCR = phi.codomain()
                         Ik = flatCR.ideal(1)
@@ -4881,7 +4881,7 @@ def periodic_points(self, n, minimal=True, formal=False, R=None, algorithm='vari
             raise NotImplementedError('periodic points not implemented for fraction function fields; '
                 'clear denominators and use the polynomial ring instead')
         if isinstance(R, FractionField_generic):
-            if is_MPolynomialRing(R.ring()):
+            if isinstance(R.ring(), MPolynomialRing_base):
                 raise NotImplementedError('periodic points not implemented for fraction function fields; '
                     'clear denominators and use the polynomial ring instead')
         CR = f_sub.coordinate_ring()
@@ -4954,7 +4954,7 @@ def periodic_points(self, n, minimal=True, formal=False, R=None, algorithm='vari
                         for k in ZZ(n).divisors():
                             if ZZ(n/k).is_prime():
                                 Sn.append(k)
-                        if (is_PolynomialRing(R) or is_MPolynomialRing(R)):
+                        if (isinstance(R, PolynomialRing_general) or isinstance(R, MPolynomialRing_base)):
                             phi = FlatteningMorphism(CR)
                             flatCR = phi.codomain()
                             Ik = flatCR.ideal(1)
@@ -5785,7 +5785,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
                 else:
                     F = base_ring
                     if isinstance(base_ring, FractionField_generic):
-                        if is_MPolynomialRing(base_ring.ring()) or is_PolynomialRing(base_ring.ring()):
+                        if isinstance(base_ring.ring(), MPolynomialRing_base) or isinstance(base_ring.ring(), PolynomialRing_general):
                             f.normalize_coordinates()
                             f_ring = f.change_ring(base_ring.ring())
                             X = f_ring.periodic_points(n, minimal=False, formal=formal, return_scheme=True)
@@ -5888,7 +5888,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
         base_ring = dom.base_ring()
         if isinstance(base_ring, FractionField_generic):
             base_ring = base_ring.ring()
-        if (is_PolynomialRing(base_ring) or is_MPolynomialRing(base_ring)):
+        if (isinstance(base_ring, PolynomialRing_general) or isinstance(base_ring, MPolynomialRing_base)):
             base_ring = base_ring.base_ring()
         elif base_ring in FunctionFields():
             base_ring = base_ring.constant_base_field()
@@ -8437,6 +8437,14 @@ def normal_form(self, return_conjugation=False):
               To:   Finite Field in z2 of size 3^2
               Defn: 1 |--> 1
 
+        Fixes :issue:`38012` by not forcing univariate polynomial to be univariate::
+
+            sage: R.<z> = PolynomialRing(QQ)
+            sage: f = DynamicalSystem_affine(z^2 + z + 1).homogenize(1)
+            sage: f.normal_form()
+            Dynamical System of Projective Space of dimension 1 over Rational Field
+             Defn: Defined on coordinates by sending (x0 : x1) to
+                   (x0^2 + 5/4*x1^2 : x1^2)
         """
         # defines the field of fixed points
         if self.codomain().dimension_relative() != 1:
@@ -8465,7 +8473,8 @@ def normal_form(self, return_conjugation=False):
         #we find one and not go all the way to the splitting field
         i = 0
         if G.degree() != 0:
-            G = G.polynomial(G.variable(0))
+            if isinstance(G.parent(), MPolynomialRing_base):
+                G = G.polynomial(G.variable(0))
         else:
             #no other fixed points
             raise NotImplementedError("map is not a polynomial")
diff --git a/src/sage/ext/fast_callable.pyx b/src/sage/ext/fast_callable.pyx
index 9d2db75be3d..48c736fff93 100644
--- a/src/sage/ext/fast_callable.pyx
+++ b/src/sage/ext/fast_callable.pyx
@@ -475,9 +475,9 @@ def fast_callable(x, domain=None, vars=None,
             x = x.function(*vars)
 
         if vars is None:
-            from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-            from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-            if is_PolynomialRing(x.parent()) or is_MPolynomialRing(x.parent()):
+            from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+            from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
+            if isinstance(x.parent(), PolynomialRing_general) or isinstance(x.parent(), MPolynomialRing_base):
                 vars = x.parent().variable_names()
             else:
                 # constant
diff --git a/src/sage/interfaces/singular.py b/src/sage/interfaces/singular.py
index c0ab80e0a68..5dd0672c137 100644
--- a/src/sage/interfaces/singular.py
+++ b/src/sage/interfaces/singular.py
@@ -1797,7 +1797,7 @@ def sage_poly(self, R=None, kcache=None):
         # TODO: Refactor imports to move this to the top
         from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_polydict
         from sage.rings.polynomial.multi_polynomial_libsingular import MPolynomialRing_libsingular
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
         from sage.rings.polynomial.polydict import ETuple
         from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
         from sage.rings.quotient_ring import QuotientRing_generic
@@ -1888,7 +1888,7 @@ def sage_poly(self, R=None, kcache=None):
 
             return R(sage_repr)
 
-        elif is_PolynomialRing(R) and (ring_is_fine or can_convert_to_singular(R)):
+        elif isinstance(R, PolynomialRing_general) and (ring_is_fine or can_convert_to_singular(R)):
 
             sage_repr = [0] * int(self.deg() + 1)
 
diff --git a/src/sage/matrix/matrix_space.py b/src/sage/matrix/matrix_space.py
index 71eb305c2be..038b7673561 100644
--- a/src/sage/matrix/matrix_space.py
+++ b/src/sage/matrix/matrix_space.py
@@ -298,7 +298,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
             except ImportError:
                 pass
             else:
-                if polynomial_ring.is_PolynomialRing(R) and R.base_ring() in _Fields:
+                if isinstance(R, polynomial_ring.PolynomialRing_general) and R.base_ring() in _Fields:
                     try:
                         from . import matrix_polynomial_dense
                     except ImportError:
@@ -306,7 +306,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
                     else:
                         return matrix_polynomial_dense.Matrix_polynomial_dense
 
-                elif multi_polynomial_ring_base.is_MPolynomialRing(R) and R.base_ring() in _Fields:
+                elif isinstance(R, multi_polynomial_ring_base.MPolynomialRing_base) and R.base_ring() in _Fields:
                     try:
                         from . import matrix_mpolynomial_dense
                     except ImportError:
diff --git a/src/sage/modular/modform/hecke_operator_on_qexp.py b/src/sage/modular/modform/hecke_operator_on_qexp.py
index daf4c3bfbec..3dc270b657b 100644
--- a/src/sage/modular/modform/hecke_operator_on_qexp.py
+++ b/src/sage/modular/modform/hecke_operator_on_qexp.py
@@ -19,7 +19,7 @@
 from sage.rings.infinity import Infinity
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
-from sage.rings.power_series_ring_element import is_PowerSeries
+from sage.rings.power_series_ring_element import PowerSeries
 
 lazy_import('sage.rings.number_field.number_field', 'CyclotomicField')
 
@@ -87,7 +87,7 @@ def hecke_operator_on_qexp(f, n, k, eps=None,
         # ZZ can coerce to GF(p), but QQ can't.
         eps = DirichletGroup(1, base_ring=ZZ)[0]
     if check:
-        if not (is_PowerSeries(f) or isinstance(f, ModularFormElement)):
+        if not (isinstance(f, PowerSeries) or isinstance(f, ModularFormElement)):
             raise TypeError("f (=%s) must be a power series or modular form" % f)
         if not isinstance(eps, DirichletCharacter):
             raise TypeError("eps (=%s) must be a Dirichlet character" % eps)
@@ -235,7 +235,7 @@ def hecke_operator_on_basis(B, n, k, eps=None, already_echelonized=False):
         eps = DirichletGroup(1, R)[0]
     all_powerseries = True
     for x in B:
-        if not is_PowerSeries(x):
+        if not isinstance(x, PowerSeries):
             all_powerseries = False
     if not all_powerseries:
         raise TypeError("each element of B must be a power series")
diff --git a/src/sage/modular/modform/space.py b/src/sage/modular/modform/space.py
index 7dba1ae3a0f..5002b281518 100644
--- a/src/sage/modular/modform/space.py
+++ b/src/sage/modular/modform/space.py
@@ -70,7 +70,7 @@
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.power_series_ring import PowerSeriesRing
-from sage.rings.power_series_ring_element import is_PowerSeries
+from sage.rings.power_series_ring_element import PowerSeries
 from sage.rings.rational_field import QQ
 from sage.categories.rings import Rings
 
@@ -1121,7 +1121,7 @@ def _element_constructor_(self, x, check=True):
 
             return self(x.q_expansion(self._q_expansion_module().degree()))
 
-        elif is_PowerSeries(x):
+        elif isinstance(x, PowerSeries):
             if x.prec() == PlusInfinity():
                 if x == 0:
                     return self.element_class(self, self.free_module().zero())
@@ -1914,7 +1914,7 @@ def find_in_space(self, f, forms=None, prec=None, indep=True):
                 B = V.span_of_basis(w)
             else:
                 B = V.span(w)
-        if is_PowerSeries(f) and f.prec() < n:
+        if isinstance(f, PowerSeries) and f.prec() < n:
             raise ValueError("you need at least %s terms of precision" % n)
         x = V(f.padded_list(n))
         return B.coordinates(x)
diff --git a/src/sage/modular/modform_hecketriangle/abstract_space.py b/src/sage/modular/modform_hecketriangle/abstract_space.py
index 719d8847f31..dda22dd1b34 100644
--- a/src/sage/modular/modform_hecketriangle/abstract_space.py
+++ b/src/sage/modular/modform_hecketriangle/abstract_space.py
@@ -23,7 +23,7 @@
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.laurent_series_ring import is_LaurentSeriesRing
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.power_series_ring import is_PowerSeriesRing
 from sage.rings.rational_field import QQ
 from sage.structure.element import parent
@@ -1721,7 +1721,7 @@ def construct_form(self, laurent_series, order_1=ZZ(0), check=True, rationalize=
         """
 
         base_ring = laurent_series.base_ring()
-        if is_PolynomialRing(base_ring.base()):
+        if isinstance(base_ring.base(), PolynomialRing_general):
             if not (self.coeff_ring().has_coerce_map_from(base_ring)):
                 raise ValueError("The Laurent coefficients don't coerce into the coefficient ring of self!")
         elif rationalize:
@@ -2015,7 +2015,7 @@ def construct_quasi_form(self, laurent_series, order_1=ZZ(0), check=True, ration
         """
 
         base_ring = laurent_series.base_ring()
-        if is_PolynomialRing(base_ring.base()):
+        if isinstance(base_ring.base(), PolynomialRing_general):
             if not (self.coeff_ring().has_coerce_map_from(base_ring)):
                 raise ValueError("The Laurent coefficients don't coerce into the coefficient ring of self!")
         elif rationalize:
@@ -2282,7 +2282,7 @@ def rationalize_series(self, laurent_series, coeff_bound=1e-10, denom_factor=ZZ(
 
         # If the coefficients already coerce to our coefficient ring
         # and are in polynomial form we simply return the Laurent series
-        if (is_PolynomialRing(base_ring.base())):
+        if (isinstance(base_ring.base(), PolynomialRing_general)):
             if (self.coeff_ring().has_coerce_map_from(base_ring)):
                 return laurent_series
             else:
diff --git a/src/sage/modular/modform_hecketriangle/functors.py b/src/sage/modular/modform_hecketriangle/functors.py
index b0fdfcf5ac7..caf554da0de 100644
--- a/src/sage/modular/modform_hecketriangle/functors.py
+++ b/src/sage/modular/modform_hecketriangle/functors.py
@@ -79,7 +79,7 @@ def _get_base_ring(ring, var_name="d"):
     """
 
     # from sage.rings.fraction_field import FractionField_generic
-    from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+    from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
     from sage.categories.pushout import FractionField as FractionFieldFunctor
 
     base_ring = ring
@@ -87,7 +87,7 @@ def _get_base_ring(ring, var_name="d"):
     #    base_ring = base_ring.base()
     if (base_ring.construction() and base_ring.construction()[0] == FractionFieldFunctor()):
         base_ring = base_ring.construction()[1]
-    if (is_PolynomialRing(base_ring) and base_ring.ngens() == 1 and base_ring.variable_name() == var_name):
+    if (isinstance(base_ring, PolynomialRing_general) and base_ring.ngens() == 1 and base_ring.variable_name() == var_name):
         base_ring = base_ring.base()
     if (base_ring.construction() and base_ring.construction()[0] == FractionFieldFunctor()):
         base_ring = base_ring.construction()[1]
diff --git a/src/sage/rings/asymptotic/asymptotic_ring.py b/src/sage/rings/asymptotic/asymptotic_ring.py
index d85f407872f..3eff60575f7 100644
--- a/src/sage/rings/asymptotic/asymptotic_ring.py
+++ b/src/sage/rings/asymptotic/asymptotic_ring.py
@@ -4078,8 +4078,8 @@ def _element_constructor_(self, data, simplify=True, convert=True):
 
         from .misc import combine_exceptions
         from sage.symbolic.ring import SymbolicRing
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
         from sage.rings.power_series_ring import is_PowerSeriesRing
 
         if isinstance(P, SymbolicRing):
@@ -4097,7 +4097,7 @@ def _element_constructor_(self, data, simplify=True, convert=True):
                                        (data, self)), e)
                 return sum(summands, self.zero())
 
-        elif is_PolynomialRing(P):
+        elif isinstance(P, PolynomialRing_general):
             p = P.gen()
             try:
                 return sum(iter(self.create_summand('exact', growth=p**i,
@@ -4108,7 +4108,7 @@ def _element_constructor_(self, data, simplify=True, convert=True):
                 raise combine_exceptions(
                     ValueError('Polynomial %s is not in %s' % (data, self)), e)
 
-        elif is_MPolynomialRing(P):
+        elif isinstance(P, MPolynomialRing_base):
             try:
                 return sum(iter(self.create_summand('exact', growth=g, coefficient=c)
                                 for c, g in iter(data)),
diff --git a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
index f5163d394a5..dbfac432165 100644
--- a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
+++ b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
@@ -510,10 +510,10 @@ def dimension(self):
             sage: F.dimension()
             2
         """
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
         R = self.denominator_ring
-        if is_PolynomialRing(R) or is_MPolynomialRing(R):
+        if isinstance(R, PolynomialRing_general) or isinstance(R, MPolynomialRing_base):
             return R.ngens()
         raise NotImplementedError('only polynomial rings are supported as base')
 
@@ -3222,9 +3222,9 @@ def _element_constructor_(self, *args, **kwargs):
             p = numerator
             q = R(denominator)
 
-            from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-            from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
-            if is_PolynomialRing(R) or is_MPolynomialRing(R):
+            from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+            from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
+            if isinstance(R, PolynomialRing_general) or isinstance(R, MPolynomialRing_base):
                 if not R(q).is_unit():
                     # Factor denominator
                     try:
@@ -3292,9 +3292,9 @@ def _coerce_map_from_(self, P):
         from sage.rings.fraction_field import FractionField_generic
         if isinstance(P, FractionField_generic):
             B = P.base()
-            from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-            from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
-            if is_PolynomialRing(B) or is_MPolynomialRing(B):
+            from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+            from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
+            if isinstance(B, PolynomialRing_general) or isinstance(B, MPolynomialRing_base):
                 if self.base().has_coerce_map_from(B):
                     return True
 
diff --git a/src/sage/rings/asymptotic/growth_group.py b/src/sage/rings/asymptotic/growth_group.py
index 1d7d3049405..1cb36bf08d2 100644
--- a/src/sage/rings/asymptotic/growth_group.py
+++ b/src/sage/rings/asymptotic/growth_group.py
@@ -1805,9 +1805,9 @@ def _initial_category_(base):
         # The following block can be removed once #19269 is fixed.
         from sage.rings.integer_ring import ZZ
         from sage.rings.rational_field import QQ
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
         if base is ZZ or base is QQ or \
-                is_PolynomialRing(base) and \
+                isinstance(base, PolynomialRing_general) and \
                 (base.base_ring() is ZZ or base.base_ring() is QQ):
             return Posets()
         else:
diff --git a/src/sage/rings/asymptotic/misc.py b/src/sage/rings/asymptotic/misc.py
index c33ea3e5a94..3d01676282c 100644
--- a/src/sage/rings/asymptotic/misc.py
+++ b/src/sage/rings/asymptotic/misc.py
@@ -149,8 +149,8 @@ def parent_to_repr_short(P):
     from sage.rings.real_mpfi import RIF
     from sage.rings.real_mpfr import RR
     from sage.symbolic.ring import SR
-    from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-    from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
+    from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+    from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
     from sage.rings.power_series_ring import is_PowerSeriesRing
 
     def abbreviate(P):
@@ -168,7 +168,7 @@ def abbreviate(P):
             pass
         raise ValueError('Cannot abbreviate %s.' % (P,))
 
-    poly = is_PolynomialRing(P) or is_MPolynomialRing(P)
+    poly = isinstance(P, PolynomialRing_general) or isinstance(P, MPolynomialRing_base)
     from sage.rings import multi_power_series_ring
     power = is_PowerSeriesRing(P) or \
             multi_power_series_ring.is_MPowerSeriesRing(P)
diff --git a/src/sage/rings/finite_rings/residue_field.pyx b/src/sage/rings/finite_rings/residue_field.pyx
index 7a7fa6dfc23..b9663dd0f08 100644
--- a/src/sage/rings/finite_rings/residue_field.pyx
+++ b/src/sage/rings/finite_rings/residue_field.pyx
@@ -182,14 +182,14 @@ from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.rings.finite_rings.finite_field_constructor import zech_log_bound, FiniteField as GF
 from sage.rings.finite_rings.finite_field_prime_modn import FiniteField_prime_modn
-from sage.rings.ideal import is_Ideal
+from sage.rings.ideal import Ideal_generic
 from sage.rings.number_field.number_field_element_base import NumberFieldElement_base
 from sage.rings.number_field.number_field_ideal import NumberFieldIdeal
 
 from sage.rings.fraction_field import FractionField_generic
 
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.polynomial.polynomial_element import Polynomial
 
 from sage.structure.element cimport Element, parent, Vector
@@ -322,7 +322,7 @@ class ResidueFieldFactory(UniqueFactory):
             Residue field in abar of Fractional ideal (2*a^2 + 3*a - 10)
         """
         if check:
-            if not is_Ideal(p):
+            if not isinstance(p, Ideal_generic):
                 if isinstance(p, (int, Integer, Rational)):
                     p = ZZ.ideal(p)
                 elif isinstance(p, NumberFieldElement_base):
@@ -339,7 +339,7 @@ class ResidueFieldFactory(UniqueFactory):
                     raise ValueError("p must be an ideal or element of a number field or function field.")
             if not p.is_prime():
                 raise ValueError("p (%s) must be prime" % p)
-            if is_PolynomialRing(p.ring()):
+            if isinstance(p.ring(), PolynomialRing_general):
                 if not p.ring().base_ring().is_finite():
                     raise ValueError("residue fields only supported for polynomial rings over finite fields")
                 if not p.ring().base_ring().is_prime_field():
@@ -375,7 +375,7 @@ class ResidueFieldFactory(UniqueFactory):
 
         if pring is ZZ:
             return ResidueFiniteField_prime_modn(p, names, p.gen(), None, None, None)
-        if is_PolynomialRing(pring):
+        if isinstance(pring, PolynomialRing_general):
             K = pring.fraction_field()
             Kbase = pring.base_ring()
             f = p.gen()
@@ -1403,7 +1403,7 @@ cdef class ResidueFieldHomomorphism_global(RingHomomorphism):
         # No special code for residue fields of Z, since we just use the normal reduction map to GF(p)
         if self._K is ZZ:
             return self._F(x)
-        if is_PolynomialRing(self._K):
+        if isinstance(self._K, PolynomialRing_general):
             p = self._F.p.gen()
             if p.degree() == 1:
                 return self._F((x % p)[0])
@@ -1661,7 +1661,7 @@ cdef class LiftingMap(Section):
                 return self._K(self._K.ring_of_integers()(x))
             else:
                 return self._K(self._K.ring_of_integers()(x.polynomial().list()))
-        elif is_PolynomialRing(self._K):
+        elif isinstance(self._K, PolynomialRing_general):
             return self._K(x.polynomial().list())
         # Else the lifting map is just x |--> to_order(x * PB)
         x = self._F(x)
diff --git a/src/sage/rings/function_field/valuation.py b/src/sage/rings/function_field/valuation.py
index 5bd32b7901e..c9d4f1bbe6f 100644
--- a/src/sage/rings/function_field/valuation.py
+++ b/src/sage/rings/function_field/valuation.py
@@ -242,8 +242,8 @@ def create_key_and_extra_args(self, domain, prime):
             # unique extension to domain
             base_valuation = domain.base_field().valuation(prime)
             return self.create_key_and_extra_args_from_valuation(domain, base_valuation)
-        from sage.rings.ideal import is_Ideal
-        if is_Ideal(prime):
+        from sage.rings.ideal import Ideal_generic
+        if isinstance(prime, Ideal_generic):
             raise NotImplementedError("a place cannot be given by an ideal yet")
 
         raise NotImplementedError("argument must be a place or a pseudo-valuation on a supported subring but %r does not satisfy this for the domain %r" % (prime, domain))
diff --git a/src/sage/rings/homset.py b/src/sage/rings/homset.py
index 6e3126d7ebd..9b4a072e901 100644
--- a/src/sage/rings/homset.py
+++ b/src/sage/rings/homset.py
@@ -55,9 +55,9 @@ def RingHomset(R, S, category=None):
         Set of Homomorphisms from Integer Ring to Rational Field
 
     """
-    if quotient_ring.is_QuotientRing(R):
-        from .polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
-        if not is_PolynomialQuotientRing(R):  # backwards compatibility
+    if isinstance(R, quotient_ring.QuotientRing_nc):
+        from .polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
+        if not isinstance(R, PolynomialQuotientRing_generic):  # backwards compatibility
             return RingHomset_quo_ring(R, S, category=category)
     return RingHomset_generic(R, S, category=category)
 
diff --git a/src/sage/rings/ideal.py b/src/sage/rings/ideal.py
index ccb9128a540..9ef03a7133d 100644
--- a/src/sage/rings/ideal.py
+++ b/src/sage/rings/ideal.py
@@ -222,6 +222,9 @@ def is_Ideal(x):
         sage: from sage.rings.ideal import is_Ideal
         sage: R = ZZ
         sage: is_Ideal(R)
+        doctest:warning...
+        DeprecationWarning: The function is_Ideal is deprecated; use 'isinstance(..., Ideal_generic)' instead.
+        See https://github.com/sagemath/sage/issues/38266 for details.
         False
         sage: 1*R; is_Ideal(1*R)
         Principal ideal (1) of Integer Ring
@@ -240,6 +243,10 @@ def is_Ideal(x):
         sage: is_Ideal((x^2 + 1)*R)
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38266,
+                "The function is_Ideal is deprecated; "
+                "use 'isinstance(..., Ideal_generic)' instead.")
     return isinstance(x, Ideal_generic)
 
 
diff --git a/src/sage/rings/integer_ring.pyx b/src/sage/rings/integer_ring.pyx
index a1574d00756..77e0be1dd79 100644
--- a/src/sage/rings/integer_ring.pyx
+++ b/src/sage/rings/integer_ring.pyx
@@ -958,7 +958,7 @@ cdef class IntegerRing_class(CommutativeRing):
         """
         if isinstance(I, sage.rings.integer.Integer):
             n = I
-        elif sage.rings.ideal.is_Ideal(I):
+        elif isinstance(I, sage.rings.ideal.Ideal_generic):
             if not (I.ring() is self):
                 raise TypeError("I must be an ideal of ZZ")
             n = I.gens()[0]
@@ -1027,7 +1027,7 @@ cdef class IntegerRing_class(CommutativeRing):
         """
         if isinstance(prime, sage.rings.integer.Integer):
             p = self.ideal(prime)
-        elif sage.rings.ideal.is_Ideal(prime):
+        elif isinstance(prime, sage.rings.ideal.Ideal_generic):
             if not (prime.ring() is self):
                 raise TypeError("%s is not an ideal of ZZ" % prime)
             p = prime
diff --git a/src/sage/rings/laurent_series_ring.py b/src/sage/rings/laurent_series_ring.py
index e2b03bcca58..6e8e8a932b0 100644
--- a/src/sage/rings/laurent_series_ring.py
+++ b/src/sage/rings/laurent_series_ring.py
@@ -678,13 +678,13 @@ def _coerce_map_from_(self, P):
         from sage.rings.polynomial.laurent_polynomial_ring_base import (
             LaurentPolynomialRing_generic,
         )
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
         from sage.rings.power_series_ring import is_PowerSeriesRing
 
         if ((is_LaurentSeriesRing(P) or
              isinstance(P, LaurentPolynomialRing_generic) or
              is_PowerSeriesRing(P) or
-             is_PolynomialRing(P))
+             isinstance(P, PolynomialRing_general))
             and P.variable_name() == self.variable_name()
             and A.has_coerce_map_from(P.base_ring())):
             return True
diff --git a/src/sage/rings/laurent_series_ring_element.pyx b/src/sage/rings/laurent_series_ring_element.pyx
index 62c244d1669..18dfe49843f 100644
--- a/src/sage/rings/laurent_series_ring_element.pyx
+++ b/src/sage/rings/laurent_series_ring_element.pyx
@@ -78,6 +78,10 @@ from sage.misc.derivative import multi_derivative
 
 
 def is_LaurentSeries(x):
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38266,
+                       "The function is_LaurentSeries is deprecated; "
+                       "use 'isinstance(..., LaurentSeries)' instead.")
     return isinstance(x, LaurentSeries)
 
 
diff --git a/src/sage/rings/morphism.pyx b/src/sage/rings/morphism.pyx
index bad89829a70..23942100ac0 100644
--- a/src/sage/rings/morphism.pyx
+++ b/src/sage/rings/morphism.pyx
@@ -898,7 +898,7 @@ cdef class RingHomomorphism(RingMap):
             Ideal (xx, xx*yy + 3*xx) of Quotient of Multivariate Polynomial Ring
              in x, y over Rational Field by the ideal (x^2, y^2)
         """
-        if not ideal.is_Ideal(I):
+        if not isinstance(I, ideal.Ideal_generic):
             raise TypeError("I must be an ideal")
         R = self.codomain()
         return R.ideal([self(y) for y in I.gens()])
@@ -1038,10 +1038,10 @@ cdef class RingHomomorphism(RingMap):
             sage: f.kernel()                                                            # needs sage.libs.singular
             Ideal (0) of Multivariate Polynomial Ring in t, u over Rational Field
         """
-        from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
-        from sage.rings.quotient_ring import is_QuotientRing
-        from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+        from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
+        from sage.rings.quotient_ring import QuotientRing_nc
+        from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
         B = self.codomain()
         graph, from_B, to_A = self._graph_ideal()
         Q = graph.ring()
@@ -1050,14 +1050,14 @@ cdef class RingHomomorphism(RingMap):
             # avoid adding the 0-ideal to the graph ideal in order to benefit
             # from a cached Gröbner basis
             graph_I = graph
-        elif (is_MPolynomialRing(B) or is_PolynomialRing(B)
-              or is_QuotientRing(B) or is_PolynomialQuotientRing(B)):
+        elif (isinstance(B, MPolynomialRing_base) or isinstance(B, PolynomialRing_general)
+              or isinstance(B, QuotientRing_nc) or isinstance(B, PolynomialQuotientRing_generic)):
             graph_I = graph + from_B(I)
         else:
             # non-zero fractional ideals of number fields not yet supported
             raise NotImplementedError("inverse image not implemented "
                                       "for ideals in %s" % B)
-        if is_QuotientRing(Q):
+        if isinstance(Q, QuotientRing_nc):
             # elimination_ideal does not work with quotient rings, so
             # switch to the cover ring
             gens_B_lifted = Q.cover_ring().gens()[:B.ngens()]
@@ -1287,7 +1287,7 @@ cdef class RingHomomorphism(RingMap):
             ...
             NotImplementedError: rings are not commutative
         """
-        from sage.rings.quotient_ring import is_QuotientRing
+        from sage.rings.quotient_ring import QuotientRing_nc
         from sage.rings.ideal import Ideal_generic
         A = self.domain()
         B = self.codomain()
@@ -1306,7 +1306,7 @@ cdef class RingHomomorphism(RingMap):
         A_to_Q = A.hom(Q.gens()[B.ngens():], Q, check=False)
         B_to_Q = B.hom(Q.gens()[:B.ngens()], Q, check=False)
         graph = Q.ideal([B_to_Q(self(x)) - A_to_Q(x) for x in A.gens()])
-        R = Q.cover_ring() if is_QuotientRing(Q) else Q
+        R = Q.cover_ring() if isinstance(Q, QuotientRing_nc) else Q
         R_to_A = R.hom(tuple([0] * B.ngens()) + A.gens(), A, check=False)
         Q_to_A = R_to_A if R is Q else R_to_A * Q.lifting_map()
 
@@ -3139,12 +3139,12 @@ def _tensor_product_ring(B, A):
     """
     from sage.rings.finite_rings.finite_field_base import FiniteField
     from sage.rings.number_field.number_field_base import NumberField
-    from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-    from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
-    from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+    from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
+    from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
+    from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
     from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
     from sage.rings.polynomial.term_order import TermOrder
-    from sage.rings.quotient_ring import is_QuotientRing
+    from sage.rings.quotient_ring import QuotientRing_nc
 
     if set(B.variable_names()).isdisjoint(A.variable_names()):
         names = B.variable_names() + A.variable_names()
@@ -3154,7 +3154,7 @@ def _tensor_product_ring(B, A):
 
     def term_order(A):
         # univariate rings do not have a term order
-        if (is_PolynomialRing(A) or is_PolynomialQuotientRing(A)
+        if (isinstance(A, PolynomialRing_general) or isinstance(A, PolynomialQuotientRing_generic)
             or (isinstance(A, (NumberField, FiniteField))
                 and not A.is_prime_field())):
             return TermOrder('lex', 1)
@@ -3170,12 +3170,12 @@ def _tensor_product_ring(B, A):
                        order=term_order(B) + term_order(A))
 
     def relations(A, R_gens_A):
-        if is_MPolynomialRing(A) or is_PolynomialRing(A):
+        if isinstance(A, MPolynomialRing_base) or isinstance(A, PolynomialRing_general):
             return []
-        elif is_PolynomialQuotientRing(A):
+        elif isinstance(A, PolynomialQuotientRing_generic):
             to_R = A.ambient().hom(R_gens_A, R, check=False)
             return [to_R(A.modulus())]
-        elif is_QuotientRing(A):
+        elif isinstance(A, QuotientRing_nc):
             to_R = A.ambient().hom(R_gens_A, R, check=False)
             return list(to_R(A.defining_ideal()).gens())
         elif (isinstance(A, (NumberField, FiniteField))
diff --git a/src/sage/rings/multi_power_series_ring.py b/src/sage/rings/multi_power_series_ring.py
index d399fdb6c0b..ab2b35d718c 100644
--- a/src/sage/rings/multi_power_series_ring.py
+++ b/src/sage/rings/multi_power_series_ring.py
@@ -207,9 +207,9 @@
 
 from sage.rings.infinity import infinity
 from sage.rings.multi_power_series_ring_element import MPowerSeries
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
 from sage.rings.polynomial.term_order import TermOrder
 from sage.rings.power_series_ring import PowerSeriesRing, PowerSeriesRing_generic, is_PowerSeriesRing
 from sage.rings.ring import CommutativeRing
@@ -663,8 +663,8 @@ def _coerce_impl(self, f):
             True
         """
         P = f.parent()
-        if is_MPolynomialRing(P) or is_MPowerSeriesRing(P) \
-               or is_PolynomialRing(P) or is_PowerSeriesRing(P):
+        if isinstance(P, MPolynomialRing_base) or is_MPowerSeriesRing(P) \
+               or isinstance(P, PolynomialRing_general) or is_PowerSeriesRing(P):
             if set(P.variable_names()).issubset(set(self.variable_names())):
                 if self.has_coerce_map_from(P.base_ring()):
                     return self(f)
@@ -827,8 +827,8 @@ def _coerce_map_from_(self, P):
             sage: R.has_coerce_map_from(L)
             True
         """
-        if is_MPolynomialRing(P) or is_MPowerSeriesRing(P) \
-                   or is_PolynomialRing(P) or is_PowerSeriesRing(P):
+        if isinstance(P, MPolynomialRing_base) or is_MPowerSeriesRing(P) \
+                   or isinstance(P, PolynomialRing_general) or is_PowerSeriesRing(P):
             if set(P.variable_names()).issubset(set(self.variable_names())):
                 if self.has_coerce_map_from(P.base_ring()):
                     return True
diff --git a/src/sage/rings/multi_power_series_ring_element.py b/src/sage/rings/multi_power_series_ring_element.py
index 32e16def317..72cb8b4a2d8 100644
--- a/src/sage/rings/multi_power_series_ring_element.py
+++ b/src/sage/rings/multi_power_series_ring_element.py
@@ -159,7 +159,7 @@
 from sage.rings.finite_rings.integer_mod_ring import Zmod
 from sage.rings.infinity import infinity, is_Infinite
 from sage.rings.integer import Integer
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.power_series_ring import is_PowerSeriesRing
 from sage.rings.power_series_ring_element import PowerSeries
 
@@ -174,8 +174,14 @@ def is_MPowerSeries(f):
         sage: from sage.rings.multi_power_series_ring_element import is_MPowerSeries
         sage: M = PowerSeriesRing(ZZ,4,'v')
         sage: is_PowerSeries(M.random_element(10))
+        doctest:warning...
+        DeprecationWarning: The function is_PowerSeries is deprecated; use 'isinstance(..., PowerSeries)' instead.
+        See https://github.com/sagemath/sage/issues/38266 for details.
         True
         sage: is_MPowerSeries(M.random_element(10))
+        doctest:warning...
+        DeprecationWarning: The function is_MPowerSeries is deprecated; use 'isinstance(..., MPowerSeries)' instead.
+        See https://github.com/sagemath/sage/issues/38266 for details.
         True
         sage: T.<v> = PowerSeriesRing(RR)
         sage: is_MPowerSeries(1 - v + v^2 +O(v^3))
@@ -183,6 +189,10 @@ def is_MPowerSeries(f):
         sage: is_PowerSeries(1 - v + v^2 +O(v^3))
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38266,
+                "The function is_MPowerSeries is deprecated; "
+                "use 'isinstance(..., MPowerSeries)' instead.")
     return isinstance(f, MPowerSeries)
 
 
@@ -369,7 +379,7 @@ def __init__(self, parent, x=0, prec=infinity, is_gen=False, check=False):
             # x is either a multivariate or univariate power series
             #
             # test whether x coerces directly to designated parent
-            if is_MPowerSeries(x):
+            if isinstance(x, MPowerSeries):
                 try:
                     self._bg_value = parent._bg_ps_ring(x._bg_value)
                 except TypeError:
@@ -393,7 +403,7 @@ def __init__(self, parent, x=0, prec=infinity, is_gen=False, check=False):
                 self._bg_value = parent._send_to_bg(x).add_bigoh(prec)
 
         # test whether x coerces to underlying polynomial ring of parent
-        elif is_PolynomialRing(xparent):
+        elif isinstance(xparent, PolynomialRing_general):
             self._bg_value = parent._send_to_bg(x).add_bigoh(prec)
 
         else:
diff --git a/src/sage/rings/padics/padic_valuation.py b/src/sage/rings/padics/padic_valuation.py
index 1cf29093ba6..757786a6300 100644
--- a/src/sage/rings/padics/padic_valuation.py
+++ b/src/sage/rings/padics/padic_valuation.py
@@ -122,7 +122,7 @@ def create_key_and_extra_args(self, R, prime=None, approximants=None):
         from sage.rings.rational_field import QQ
         from sage.rings.padics.padic_generic import pAdicGeneric
         from sage.rings.number_field.number_field_base import NumberField
-        from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
+        from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
 
         if R.characteristic() != 0:
             # We do not support equal characteristic yet
@@ -132,7 +132,7 @@ def create_key_and_extra_args(self, R, prime=None, approximants=None):
             return self.create_key_for_integers(R, prime), {}
         elif isinstance(R, pAdicGeneric):
             return self.create_key_for_local_ring(R, prime), {}
-        elif isinstance(R.fraction_field(), NumberField) or is_PolynomialQuotientRing(R):
+        elif isinstance(R.fraction_field(), NumberField) or isinstance(R, PolynomialQuotientRing_generic):
             return self.create_key_and_extra_args_for_number_field(R, prime, approximants=approximants)
         else:
             raise NotImplementedError("p-adic valuations not implemented for %r" % (R,))
@@ -362,13 +362,13 @@ def _normalize_number_field_data(self, R):
              x^2 + 1)
 
         """
-        from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
+        from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
         from sage.rings.number_field.number_field_base import NumberField
         if isinstance(R.fraction_field(), NumberField):
             L = R.fraction_field()
             G = L.relative_polynomial()
             K = L.base_ring()
-        elif is_PolynomialQuotientRing(R):
+        elif isinstance(R, PolynomialQuotientRing_generic):
             from sage.categories.number_fields import NumberFields
             if R.base_ring().fraction_field() not in NumberFields():
                 raise NotImplementedError("cannot normalize quotients over %r" % (R.base_ring(),))
@@ -394,7 +394,7 @@ def create_object(self, version, key, **extra_args):
         from sage.rings.rational_field import QQ
         from sage.rings.padics.padic_generic import pAdicGeneric
         from sage.rings.valuation.valuation_space import DiscretePseudoValuationSpace
-        from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
+        from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
         from sage.rings.number_field.number_field_base import NumberField
         R = key[0]
         parent = DiscretePseudoValuationSpace(R)
@@ -412,7 +412,7 @@ def create_object(self, version, key, **extra_args):
             K = R.fraction_field()
             if isinstance(K, NumberField):
                 G = K.relative_polynomial()
-            elif is_PolynomialQuotientRing(R):
+            elif isinstance(R, PolynomialQuotientRing_generic):
                 G = R.modulus()
             else:
                 raise NotImplementedError
@@ -570,8 +570,8 @@ def is_unramified(self, G, include_steps=False, assume_squarefree=False):
         """
         R = G.parent()
 
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if not is_PolynomialRing(R) or R.base_ring() is not self.domain() or not G.is_monic():
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if not isinstance(R, PolynomialRing_general) or R.base_ring() is not self.domain() or not G.is_monic():
             raise ValueError("G must be a monic univariate polynomial over the domain of this valuation")
         if not assume_squarefree and not G.is_squarefree():
             raise ValueError("G must be squarefree")
@@ -668,8 +668,8 @@ def is_totally_ramified(self, G, include_steps=False, assume_squarefree=False):
         """
         R = G.parent()
 
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if not is_PolynomialRing(R) or R.base_ring() is not self.domain() or not G.is_monic():
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if not isinstance(R, PolynomialRing_general) or R.base_ring() is not self.domain() or not G.is_monic():
             raise ValueError("G must be a monic univariate polynomial over the domain of this valuation")
         if not assume_squarefree and not G.is_squarefree():
             raise ValueError("G must be squarefree")
@@ -800,9 +800,9 @@ def extensions(self, ring):
             if domain_fraction_field.is_subring(ring):
                 return pAdicValuation(domain_fraction_field, self).extensions(ring)
         if self.domain().is_subring(ring):
-            from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
-            if is_PolynomialQuotientRing(ring):
-                if is_PolynomialQuotientRing(self.domain()):
+            from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
+            if isinstance(ring, PolynomialQuotientRing_generic):
+                if isinstance(self.domain(), PolynomialQuotientRing_generic):
                     if self.domain().modulus() == ring.modulus():
                         base_extensions = self._base_valuation.extensions(self._base_valuation.domain().change_ring(self._base_valuation.domain().base_ring().fraction_field()))
                         return [pAdicValuation(ring, base._initial_approximation) for base in base_extensions]
@@ -1463,8 +1463,8 @@ def _fraction_field(ring):
     if ring in Fields():
         return ring
 
-    from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
-    if is_PolynomialQuotientRing(ring):
+    from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
+    if isinstance(ring, PolynomialQuotientRing_generic):
         from sage.categories.integral_domains import IntegralDomains
         if ring in IntegralDomains():
             return ring.base().change_ring(ring.base_ring().fraction_field()).quo(ring.modulus())
diff --git a/src/sage/rings/polynomial/flatten.py b/src/sage/rings/polynomial/flatten.py
index ef71d2b13a6..da8da019c20 100644
--- a/src/sage/rings/polynomial/flatten.py
+++ b/src/sage/rings/polynomial/flatten.py
@@ -38,8 +38,8 @@
 from sage.categories.morphism import Morphism
 from sage.misc.cachefunc import cached_method
 from .polynomial_ring_constructor import PolynomialRing
-from .polynomial_ring import is_PolynomialRing
-from .multi_polynomial_ring_base import is_MPolynomialRing
+from .polynomial_ring import PolynomialRing_general
+from .multi_polynomial_ring_base import MPolynomialRing_base
 from sage.rings.fraction_field import FractionField_generic
 from sage.rings.fraction_field_element import FractionFieldElement
 from sage.rings.polynomial.polydict import ETuple
@@ -160,14 +160,14 @@ def __init__(self, domain):
             sage: fl.section()(fl(p)) == p
             True
         """
-        if not is_PolynomialRing(domain) and not is_MPolynomialRing(domain):
+        if not isinstance(domain, PolynomialRing_general) and not isinstance(domain, MPolynomialRing_base):
             raise ValueError("domain should be a polynomial ring")
 
         ring = domain
         variables = []
         intermediate_rings = []
 
-        while is_PolynomialRing(ring) or is_MPolynomialRing(ring):
+        while isinstance(ring, PolynomialRing_general) or isinstance(ring, MPolynomialRing_base):
             intermediate_rings.append(ring)
             v = ring.variable_names()
             variables.extend(reversed(v))
@@ -181,7 +181,7 @@ def __init__(self, domain):
                     if b not in variables:  # not just variables[:i]!
                         break
                 variables[i] = b
-        if is_MPolynomialRing(domain):
+        if isinstance(domain, MPolynomialRing_base):
             codomain = PolynomialRing(ring, variables, len(variables))
         else:
             codomain = PolynomialRing(ring, variables)
@@ -221,12 +221,12 @@ def _call_(self, p):
 
         for ring in self._intermediate_rings:
             new_p = {}
-            if is_PolynomialRing(ring):
+            if isinstance(ring, PolynomialRing_general):
                 for mon, pp in p.items():
                     assert pp.parent() is ring
                     for i, j in pp.dict().items():
                         new_p[(i,)+(mon)] = j
-            elif is_MPolynomialRing(ring):
+            elif isinstance(ring, MPolynomialRing_base):
                 for mon, pp in p.items():
                     assert pp.parent() is ring
                     for mmon, q in pp.dict().items():
@@ -345,17 +345,17 @@ def __init__(self, domain, codomain):
             ...
             ValueError: rings must have the same number of variables
         """
-        if not is_MPolynomialRing(domain):
+        if not isinstance(domain, MPolynomialRing_base):
             raise ValueError("domain should be a multivariate polynomial ring")
-        if not is_PolynomialRing(codomain) and not is_MPolynomialRing(codomain):
+        if not isinstance(codomain, PolynomialRing_general) and not isinstance(codomain, MPolynomialRing_base):
             raise ValueError("codomain should be a polynomial ring")
 
         ring = codomain
         intermediate_rings = []
 
         while True:
-            is_polynomial_ring = is_PolynomialRing(ring)
-            if not (is_polynomial_ring or is_MPolynomialRing(ring)):
+            is_polynomial_ring = isinstance(ring, PolynomialRing_general)
+            if not (is_polynomial_ring or isinstance(ring, MPolynomialRing_base)):
                 break
             intermediate_rings.append((ring, is_polynomial_ring))
             ring = ring.base_ring()
@@ -499,7 +499,7 @@ def __init__(self, domain, D):
               Defn: Defined on coordinates by sending (z) to
                     (z^2 + 1.00000000000000)
         """
-        if not is_PolynomialRing(domain) and not is_MPolynomialRing(domain):
+        if not isinstance(domain, PolynomialRing_general) and not isinstance(domain, MPolynomialRing_base):
             raise TypeError("domain should be a polynomial ring")
 
         # use only the generators that are in the stack somewhere,
@@ -538,7 +538,7 @@ def __init__(self, domain, D):
         # Construct unflattened codomain R
         new_vars = []
         R = domain
-        while is_PolynomialRing(R) or is_MPolynomialRing(R) or isinstance(R, FractionField_generic):
+        while isinstance(R, PolynomialRing_general) or isinstance(R, MPolynomialRing_base) or isinstance(R, FractionField_generic):
             if isinstance(R, FractionField_generic):
                 # We've hit base_ring, so set _sub_specialization and exit the loop
                 field_over = R.base()
@@ -563,7 +563,7 @@ def __init__(self, domain, D):
             # We're still in the polynomials, so keep track of the tower
             old = R.gens()
             new = [t for t in old if t not in D]
-            force_multivariate = ((len(old) == 1) and is_MPolynomialRing(R))
+            force_multivariate = ((len(old) == 1) and isinstance(R, MPolynomialRing_base))
             new_vars.append((new, force_multivariate, old))
             R = R.base_ring()
 
diff --git a/src/sage/rings/polynomial/groebner_fan.py b/src/sage/rings/polynomial/groebner_fan.py
index 83877f35072..148d92786fd 100644
--- a/src/sage/rings/polynomial/groebner_fan.py
+++ b/src/sage/rings/polynomial/groebner_fan.py
@@ -65,7 +65,7 @@
 
 from sage.structure.sage_object import SageObject
 from sage.interfaces.gfan import gfan
-from .multi_polynomial_ideal import is_MPolynomialIdeal
+from .multi_polynomial_ideal import MPolynomialIdeal
 from .polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
 from sage.rings.integer import Integer
@@ -824,7 +824,7 @@ class to compute the Stanley-Reisner ideal of the tropical prevariety::
         if symmetry:
             print("WARNING! Symmetry option not yet implemented!!")
         self.__verbose = verbose
-        if not is_MPolynomialIdeal(I):
+        if not isinstance(I, MPolynomialIdeal):
             raise TypeError("I must be a multivariate polynomial ideal")
         if not prefix_check([str(R_gen) for R_gen in I.ring().gens()]):
             raise RuntimeError("Ring variables cannot contain each other as prefixes")
diff --git a/src/sage/rings/polynomial/laurent_polynomial.pyx b/src/sage/rings/polynomial/laurent_polynomial.pyx
index 650388e7f0f..d50daa8ecc5 100644
--- a/src/sage/rings/polynomial/laurent_polynomial.pyx
+++ b/src/sage/rings/polynomial/laurent_polynomial.pyx
@@ -13,7 +13,7 @@ from sage.structure.element import coerce_binop, parent
 from sage.structure.factorization import Factorization
 from sage.misc.derivative import multi_derivative
 from sage.rings.polynomial.polynomial_element import Polynomial
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.structure.richcmp cimport richcmp, rich_to_bool
 from sage.rings.infinity import minus_infinity
 
@@ -431,7 +431,7 @@ cdef class LaurentPolynomial_univariate(LaurentPolynomial):
         if self.__n < 0:
             raise ValueError("Laurent polynomial with negative valuation cannot be converted to polynomial")
 
-        if is_PolynomialRing(R):
+        if isinstance(R, PolynomialRing_general):
             return R(self.__u) << self.__n
         elif self.__n == 0:
             return R(self.__u)
@@ -1401,8 +1401,8 @@ cdef class LaurentPolynomial_univariate(LaurentPolynomial):
             sage: f * (t^-2 + 1) + (1/2*t^4 + 1/2*t^3) * (t^-3 + 1)
             1
         """
-        from sage.rings.ideal import is_Ideal
-        if is_Ideal(m):
+        from sage.rings.ideal import Ideal_generic
+        if isinstance(m, Ideal_generic):
             v = m.gens_reduced()
             if len(v) > 1:
                 raise NotImplementedError("only inversion modulo principal ideals implemented")
diff --git a/src/sage/rings/polynomial/laurent_polynomial_ring.py b/src/sage/rings/polynomial/laurent_polynomial_ring.py
index c10db4a39ca..10ef6777303 100644
--- a/src/sage/rings/polynomial/laurent_polynomial_ring.py
+++ b/src/sage/rings/polynomial/laurent_polynomial_ring.py
@@ -235,18 +235,18 @@ def LaurentPolynomialRing(base_ring, *args, **kwds):
            sage: (w0 + 2*w8 + w13)^2                                                    # needs sage.modules
            w0^2 + 4*w0*w8 + 4*w8^2 + 2*w0*w13 + 4*w8*w13 + w13^2
     """
-    from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-    from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
+    from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+    from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
 
     R = PolynomialRing(base_ring, *args, **kwds)
     if R in _cache:
         return _cache[R]   # put () here to re-enable weakrefs
 
-    if is_PolynomialRing(R):
+    if isinstance(R, PolynomialRing_general):
         # univariate case
         P = LaurentPolynomialRing_univariate(R)
     else:
-        assert is_MPolynomialRing(R)
+        assert isinstance(R, MPolynomialRing_base)
         P = LaurentPolynomialRing_mpair(R)
 
     _cache[R] = P
diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py
index d5b7dce9866..83ecff24c52 100644
--- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
+++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
@@ -326,6 +326,10 @@ def is_MPolynomialIdeal(x) -> bool:
     but matches Magma's behavior. ::
 
         sage: is_MPolynomialIdeal(I)
+        doctest:warning...
+        DeprecationWarning: The function is_MPolynomialIdeal is deprecated;
+        use 'isinstance(..., MPolynomialIdeal)' instead.
+        See https://github.com/sagemath/sage/issues/38266 for details.
         False
 
     ::
@@ -334,6 +338,10 @@ def is_MPolynomialIdeal(x) -> bool:
         sage: is_MPolynomialIdeal(I)
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38266,
+                "The function is_MPolynomialIdeal is deprecated; "
+                "use 'isinstance(..., MPolynomialIdeal)' instead.")
     return isinstance(x, MPolynomialIdeal)
 
 
@@ -592,12 +600,11 @@ def _groebner_cover(self):
             [[1], [1], [[[(2*a + 3)], [[1]]]]]]
         """
         from sage.rings.fraction_field import FractionField_generic
-        from sage.rings.polynomial.multi_polynomial_ring_base import \
-            is_MPolynomialRing
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+        from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
         F = self.base_ring()
         if (not isinstance(F, FractionField_generic) or
-            (not is_MPolynomialRing(F.ring()) and not is_PolynomialRing(F.ring()))):
+            not isinstance(F.ring(), (MPolynomialRing_base, PolynomialRing_general))):
             raise TypeError("the base ring must be a field with parameters")
         from sage.arith.functions import lcm
         from sage.libs.singular.function import lib, singular_function
diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
index 6b838190c52..ca305456a39 100644
--- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
@@ -218,7 +218,7 @@ from sage.rings.polynomial.multi_polynomial_ring_base import BooleanPolynomialRi
 from sage.rings.polynomial.multi_polynomial_element import MPolynomial_polydict
 from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
 from sage.rings.polynomial.polydict cimport ETuple
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 
 # base ring imports
 import sage.rings.abc
@@ -509,7 +509,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
                 return True
             elif base_ring.has_coerce_map_from(other._mpoly_base_ring(self.variable_names())):
                 return True
-        elif is_PolynomialRing(other):
+        elif isinstance(other, PolynomialRing_general):
             if base_ring.has_coerce_map_from(other._mpoly_base_ring(self.variable_names())):
                 return True
 
@@ -1099,8 +1099,8 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
         coerce = kwds.get('coerce', True)
         if len(gens) == 1:
             gens = gens[0]
-        from sage.rings.ideal import is_Ideal
-        if is_Ideal(gens):
+        from sage.rings.ideal import Ideal_generic
+        if isinstance(gens, Ideal_generic):
             if gens.ring() is self:
                 return gens
             gens = gens.gens()
diff --git a/src/sage/rings/polynomial/multi_polynomial_ring.py b/src/sage/rings/polynomial/multi_polynomial_ring.py
index 03343b85b99..20c7b68d48b 100644
--- a/src/sage/rings/polynomial/multi_polynomial_ring.py
+++ b/src/sage/rings/polynomial/multi_polynomial_ring.py
@@ -144,7 +144,7 @@ def __eq__(self, other):
             sage: loads(R.dumps()) == R
             True
         """
-        if not is_MPolynomialRing(other):
+        if not isinstance(other, MPolynomialRing_base):
             return False
         return ((self.base_ring(), self.ngens(),
                 self.variable_names(), self.term_order()) ==
@@ -943,8 +943,8 @@ def ideal(self, *gens, **kwds):
         """
         do_coerce = False
         if len(gens) == 1:
-            from sage.rings.ideal import is_Ideal
-            if is_Ideal(gens[0]):
+            from sage.rings.ideal import Ideal_generic
+            if isinstance(gens[0], Ideal_generic):
                 if gens[0].ring() is self:
                     return gens[0]
                 gens = gens[0].gens()
diff --git a/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx b/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx
index 55d2900fa61..3200f8a554c 100644
--- a/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx
@@ -29,6 +29,10 @@ from sage.rings.polynomial.polynomial_ring_constructor import (PolynomialRing,
 
 
 def is_MPolynomialRing(x):
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38266,
+                       "The function is_MPolynomialRing is deprecated; "
+                       "use 'isinstance(..., MPolynomialRing_base)' instead.")
     return isinstance(x, MPolynomialRing_base)
 
 
@@ -135,7 +139,7 @@ cdef class MPolynomialRing_base(CommutativeRing):
              Multivariate Polynomial Ring in x, y over Rational Field
         """
         base = self.base_ring()
-        if is_MPolynomialRing(base) or polynomial_ring.is_PolynomialRing(base):
+        if isinstance(base, MPolynomialRing_base) or isinstance(base, polynomial_ring.PolynomialRing_general):
             from sage.rings.polynomial.flatten import FlatteningMorphism
             return FlatteningMorphism(self)
         else:
@@ -590,14 +594,14 @@ cdef class MPolynomialRing_base(CommutativeRing):
             P = x.parent()
             # polynomial rings in the same variable over the any base
             # that coerces in:
-            if is_MPolynomialRing(P):
+            if isinstance(P, MPolynomialRing_base):
                 if P.variable_names() == self.variable_names():
                     if self.has_coerce_map_from(P.base_ring()):
                         return self(x)
                 elif self.base_ring().has_coerce_map_from(P._mpoly_base_ring(self.variable_names())):
                     return self(x)
 
-            elif polynomial_ring.is_PolynomialRing(P):
+            elif isinstance(P, polynomial_ring.PolynomialRing_general):
                 if P.variable_name() in self.variable_names():
                     if self.has_coerce_map_from(P.base_ring()):
                         return self(x)
@@ -634,7 +638,7 @@ cdef class MPolynomialRing_base(CommutativeRing):
             # One is not a parent -- not equal and not ordered
             return op == Py_NE
 
-        if not is_MPolynomialRing(right):
+        if not isinstance(right, MPolynomialRing_base):
             return op == Py_NE
 
         lft = <MPolynomialRing_base>left
diff --git a/src/sage/rings/polynomial/multi_polynomial_sequence.py b/src/sage/rings/polynomial/multi_polynomial_sequence.py
index b559993d39f..35227eb54f5 100644
--- a/src/sage/rings/polynomial/multi_polynomial_sequence.py
+++ b/src/sage/rings/polynomial/multi_polynomial_sequence.py
@@ -168,9 +168,9 @@
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.infinity import Infinity
 from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.quotient_ring import is_QuotientRing
+from sage.rings.quotient_ring import QuotientRing_nc
 from sage.structure.sequence import Sequence_generic
 
 try:
@@ -197,12 +197,17 @@ def is_PolynomialSequence(F):
         sage: F = Sequence(I, P); F
         [x^2 + y^2, x^2 - y^2]
 
-        sage: from sage.rings.polynomial.multi_polynomial_sequence import is_PolynomialSequence
-        sage: is_PolynomialSequence(F)
+        sage: from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence_generic
+        sage: isinstance(F, PolynomialSequence_generic)
         True
 
     """
-    return isinstance(F,PolynomialSequence_generic)
+    from sage.misc.superseded import deprecation
+    deprecation(38266,
+                "The function is_PolynomialSequence is deprecated; "
+                "use 'isinstance(..., PolynomialSequence_generic)' instead.")
+    return isinstance(F, PolynomialSequence_generic)
+
 
 def PolynomialSequence(arg1, arg2=None, immutable=False, cr=False, cr_str=None):
     """
@@ -297,7 +302,7 @@ def PolynomialSequence(arg1, arg2=None, immutable=False, cr=False, cr_str=None):
     except ImportError:
         BooleanMonomialMonoid = ()
 
-    is_ring = lambda r: is_MPolynomialRing(r) or isinstance(r, BooleanMonomialMonoid) or (is_QuotientRing(r) and is_MPolynomialRing(r.cover_ring()))
+    is_ring = lambda r: isinstance(r, MPolynomialRing_base) or isinstance(r, BooleanMonomialMonoid) or (isinstance(r, QuotientRing_nc) and isinstance(r.cover_ring(), MPolynomialRing_base))
 
     if is_ring(arg1):
         ring, gens = arg1, arg2
@@ -958,7 +963,7 @@ def __add__(self, right):
              b^2 + 2*a*c + 2*b*d - c,
              a^127 + a]
         """
-        if is_PolynomialSequence(right) and right.ring() == self.ring():
+        if isinstance(right, PolynomialSequence_generic) and right.ring() == self.ring():
             return PolynomialSequence(self.ring(), self.parts() + right.parts())
 
         elif isinstance(right,(tuple,list)) and all((x.parent() == self.ring() for x in right)):
diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index dcf2af7cdf2..9029427c6a1 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -118,9 +118,9 @@ from sage.arith.functions import lcm
 
 from sage.rings.polynomial import polynomial_fateman
 
-from sage.rings.ideal import is_Ideal
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.rings.ideal import Ideal_generic
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
 from sage.rings.polynomial.multi_polynomial cimport MPolynomial
 from sage.rings.polynomial.polynomial_quotient_ring_element import PolynomialQuotientRingElement
 from sage.misc.cachefunc import cached_function
@@ -1616,8 +1616,8 @@ cdef class Polynomial(CommutativePolynomial):
 
         - Robert Bradshaw (2007-05-31)
         """
-        from sage.rings.ideal import is_Ideal
-        if is_Ideal(m):
+        from sage.rings.ideal import Ideal_generic
+        if isinstance(m, Ideal_generic):
             v = m.gens_reduced()
             if len(v) > 1:
                 raise NotImplementedError("Don't know how to invert modulo non-principal ideal %s" % m)
@@ -7550,7 +7550,7 @@ cdef class Polynomial(CommutativePolynomial):
             raise TypeError("p2 must be a polynomial")
         p1, p2 = coercion_model.canonical_coercion(p1, p2)
         K = p1.parent()
-        assert is_PolynomialRing(p1.parent())
+        assert isinstance(p1.parent(), PolynomialRing_general)
         S = K.base_ring()
         Sf = S.fraction_field()
 
@@ -7984,7 +7984,7 @@ cdef class Polynomial(CommutativePolynomial):
             return self  # return 0
         n = self.degree()
         base_ring = self._parent.base_ring()
-        if (is_MPolynomialRing(base_ring) or
+        if (isinstance(base_ring, MPolynomialRing_base) or
             is_PowerSeriesRing(base_ring)):
             # It is often cheaper to compute discriminant of simple
             # multivariate polynomial and substitute the real
@@ -9988,7 +9988,7 @@ cdef class Polynomial(CommutativePolynomial):
             _p = self._parent.coerce(p)
         elif p is infinity.infinity:
             return -self.degree()
-        elif is_Ideal(p) and p.ring() is self._parent: # eventually need to handle fractional ideals in the fraction field
+        elif isinstance(p, Ideal_generic) and p.ring() is self._parent: # eventually need to handle fractional ideals in the fraction field
             if self._parent.base_ring().is_field(): # common case
                 _p = p.gen()
             else:
diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring.py b/src/sage/rings/polynomial/polynomial_quotient_ring.py
index 0ce0673ad67..e97f8b03f19 100644
--- a/src/sage/rings/polynomial/polynomial_quotient_ring.py
+++ b/src/sage/rings/polynomial/polynomial_quotient_ring.py
@@ -266,6 +266,10 @@ def create_object(self, version, key):
 PolynomialQuotientRing = PolynomialQuotientRingFactory("PolynomialQuotientRing")
 
 def is_PolynomialQuotientRing(x):
+    from sage.misc.superseded import deprecation
+    deprecation(38266,
+                "The function is_PolynomialQuotientRing is deprecated; "
+                "use 'isinstance(..., PolynomialQuotientRing_generic)' instead.")
     return isinstance(x, PolynomialQuotientRing_generic)
 
 
@@ -1342,10 +1346,10 @@ def _S_decomposition(self, S):
         if not isinstance(K, NumberField) or not self.__polynomial.is_squarefree():
             raise NotImplementedError
 
-        from sage.rings.ideal import is_Ideal
+        from sage.rings.ideal import Ideal_generic
         for p in S:
             # second check due to inconsistency over QQ - see # 7596
-            if not (is_Ideal(p)
+            if not (isinstance(p, Ideal_generic)
                     and (p.ring() is K or p.ring() is K.ring_of_integers())
                     and p.is_prime()):
                 raise TypeError("S must be a list of prime ideals of the base field.")
diff --git a/src/sage/rings/polynomial/polynomial_ring.py b/src/sage/rings/polynomial/polynomial_ring.py
index d0d2d1241ab..628bce00ba5 100644
--- a/src/sage/rings/polynomial/polynomial_ring.py
+++ b/src/sage/rings/polynomial/polynomial_ring.py
@@ -191,6 +191,10 @@ def is_PolynomialRing(x):
         sage: from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
         sage: from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
         sage: is_PolynomialRing(2)
+        doctest:warning...
+        DeprecationWarning: The function is_PolynomialRing is deprecated;
+        use 'isinstance(..., PolynomialRing_general)' instead.
+        See https://github.com/sagemath/sage/issues/38266 for details.
         False
 
     This polynomial ring is not univariate.
@@ -200,6 +204,10 @@ def is_PolynomialRing(x):
         sage: is_PolynomialRing(ZZ['x,y,z'])
         False
         sage: is_MPolynomialRing(ZZ['x,y,z'])
+        doctest:warning...
+        DeprecationWarning: The function is_MPolynomialRing is deprecated;
+        use 'isinstance(..., MPolynomialRing_base)' instead.
+        See https://github.com/sagemath/sage/issues/38266 for details.
         True
 
     ::
@@ -221,6 +229,10 @@ def is_PolynomialRing(x):
         sage: type(R)
         <class 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular'>
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38266,
+                "The function is_PolynomialRing is deprecated; "
+                "use 'isinstance(..., PolynomialRing_general)' instead.")
     return isinstance(x, PolynomialRing_general)
 
 
@@ -616,9 +628,9 @@ def flattening_morphism(self):
             sage: QQ['x'].flattening_morphism()
             Identity endomorphism of Univariate Polynomial Ring in x over Rational Field
         """
-        from .multi_polynomial_ring import is_MPolynomialRing
+        from .multi_polynomial_ring import MPolynomialRing_base
         base = self.base_ring()
-        if is_PolynomialRing(base) or is_MPolynomialRing(base):
+        if isinstance(base, PolynomialRing_general) or isinstance(base, MPolynomialRing_base):
             from .flatten import FlatteningMorphism
             return FlatteningMorphism(self)
         else:
@@ -803,7 +815,7 @@ def _coerce_map_from_(self, P):
 
         # polynomial rings in the same variable over a base that canonically
         # coerces into self.base_ring()
-        if is_PolynomialRing(P):
+        if isinstance(P, PolynomialRing_general):
             if self.construction()[0] != P.construction()[0]:
                 # Construction (including variable names) must be the
                 # same to allow coercion
@@ -842,8 +854,8 @@ def _coerce_map_from_(self, P):
             return PolynomialRingHomomorphism_from_base(RingHomset(P, self), f)
 
         # Last, we consider multivariate polynomial rings:
-        from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-        if is_MPolynomialRing(P) and self.variable_name() in P.variable_names():
+        from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
+        if isinstance(P, MPolynomialRing_base) and self.variable_name() in P.variable_names():
             P_ = P.remove_var(self.variable_name())
             return self.base_ring() != P_ and self.base_ring().has_coerce_map_from(P_)
 
@@ -1596,7 +1608,7 @@ def _Karatsuba_threshold(self):
             0
         """
         base_ring = self.base_ring()
-        if is_PolynomialRing(base_ring):
+        if isinstance(base_ring, PolynomialRing_general):
             return 0
         try:
             from sage.matrix.matrix_space import MatrixSpace
diff --git a/src/sage/rings/power_series_mpoly.pyx b/src/sage/rings/power_series_mpoly.pyx
index 714d939c30b..1acbdbd6e69 100644
--- a/src/sage/rings/power_series_mpoly.pyx
+++ b/src/sage/rings/power_series_mpoly.pyx
@@ -3,7 +3,7 @@
 from sage.rings.power_series_ring_element cimport PowerSeries
 from sage.structure.element cimport Element
 from sage.rings.infinity import infinity
-from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
 from sage.rings import power_series_poly
 
 
@@ -56,7 +56,7 @@ cdef class PowerSeries_mpoly(PowerSeries):
             # avoid having an if statement in the inner loop of a
             # doubly-nested for loop.
             d = {}
-            if is_MPolynomialRing(B):
+            if isinstance(B, MPolynomialRing_base):
                 for i in range(len(v)):
                     for n, c in v[i].dict().iteritems():
                         d[tuple(n) + (i,)] = c
diff --git a/src/sage/rings/power_series_ring.py b/src/sage/rings/power_series_ring.py
index 1052d963bdc..bc78e0d98e2 100644
--- a/src/sage/rings/power_series_ring.py
+++ b/src/sage/rings/power_series_ring.py
@@ -148,8 +148,8 @@
 )
 from sage.rings.fraction_field_element import FractionFieldElement
 from sage.rings.infinity import infinity
-from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring_base import MPolynomialRing_base
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.structure.category_object import normalize_names
 from sage.structure.element import Expression, parent
@@ -580,7 +580,7 @@ def __init__(self, base_ring, name=None, default_prec=None, sparse=False,
             K = base_ring
             names = K.variable_names() + (name,)
             self.__mpoly_ring = PolynomialRing(K.base_ring(), names=names)
-            assert is_MPolynomialRing(self.__mpoly_ring)
+            assert isinstance(self.__mpoly_ring, MPolynomialRing_base)
             self.Element = power_series_mpoly.PowerSeries_mpoly
         elif implementation == 'pari':
             from .power_series_pari import PowerSeries_pari
@@ -711,7 +711,7 @@ def _coerce_map_from_(self, S):
         """
         if self.base_ring().has_coerce_map_from(S):
             return True
-        if (is_PolynomialRing(S) or is_PowerSeriesRing(S)) and self.base_ring().has_coerce_map_from(S.base_ring()) \
+        if (isinstance(S, PolynomialRing_general) or is_PowerSeriesRing(S)) and self.base_ring().has_coerce_map_from(S.base_ring()) \
            and self.variable_names() == S.variable_names():
             return True
 
diff --git a/src/sage/rings/power_series_ring_element.pyx b/src/sage/rings/power_series_ring_element.pyx
index 8e1b76a7cc9..f05ef305d81 100644
--- a/src/sage/rings/power_series_ring_element.pyx
+++ b/src/sage/rings/power_series_ring_element.pyx
@@ -125,6 +125,9 @@ def is_PowerSeries(x):
         sage: R.<x> = PowerSeriesRing(ZZ)
         sage: from sage.rings.power_series_ring_element import is_PowerSeries
         sage: is_PowerSeries(1 + x^2)
+        doctest:warning...
+        DeprecationWarning: The function is_PowerSeries is deprecated; use 'isinstance(..., PowerSeries)' instead.
+        See https://github.com/sagemath/sage/issues/38266 for details.
         True
         sage: is_PowerSeries(x - x)
         True
@@ -135,6 +138,10 @@ def is_PowerSeries(x):
         sage: is_PowerSeries(1 + x^2)                                                   # needs sage.symbolic
         False
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38266,
+                       "The function is_PowerSeries is deprecated; "
+                       "use 'isinstance(..., PowerSeries)' instead.")
     return isinstance(x, PowerSeries)
 
 
diff --git a/src/sage/rings/qqbar_decorators.py b/src/sage/rings/qqbar_decorators.py
index 13d6d562824..7343a0b9b08 100644
--- a/src/sage/rings/qqbar_decorators.py
+++ b/src/sage/rings/qqbar_decorators.py
@@ -86,13 +86,13 @@ def wrapper(*args, **kwds):
         from sage.misc.flatten import flatten
         from sage.rings.polynomial.polynomial_element import Polynomial
         from sage.rings.polynomial.multi_polynomial import MPolynomial
-        from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence, is_PolynomialSequence
+        from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence, PolynomialSequence_generic
         from sage.rings.ideal import Ideal, Ideal_generic
         from sage.rings.abc import AlgebraicField_common
 
         if not any(isinstance(a, (Polynomial, MPolynomial, Ideal_generic))
                    and isinstance(a.base_ring(), AlgebraicField_common)
-                   or is_PolynomialSequence(a)
+                   or isinstance(a, PolynomialSequence_generic)
                    and isinstance(a.ring().base_ring(), AlgebraicField_common) for a in args):
             return func(*args, **kwds)
 
@@ -123,7 +123,7 @@ def forward_map(item):
                 return item.map_coefficients(elem_dict.__getitem__, new_base_ring=numfield)
             elif isinstance(item, MPolynomial):
                 return item.map_coefficients(elem_dict.__getitem__, new_base_ring=numfield)
-            elif is_PolynomialSequence(item):
+            elif isinstance(item, PolynomialSequence_generic):
                 return PolynomialSequence(map(forward_map, item),
                                           immutable=item.is_immutable())
             elif isinstance(item, list):
@@ -144,7 +144,7 @@ def reverse_map(item):
                 return item.map_coefficients(morphism)
             elif isinstance(item, MPolynomial):
                 return item.map_coefficients(morphism)
-            elif is_PolynomialSequence(item):
+            elif isinstance(item, PolynomialSequence_generic):
                 return PolynomialSequence(map(reverse_map, item),
                                           immutable=item.is_immutable())
             elif isinstance(item, list):
diff --git a/src/sage/rings/quotient_ring.py b/src/sage/rings/quotient_ring.py
index 468f81115b7..49f2336cfb3 100644
--- a/src/sage/rings/quotient_ring.py
+++ b/src/sage/rings/quotient_ring.py
@@ -351,6 +351,10 @@ def is_QuotientRing(x):
         sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
         sage: S = R.quotient_ring(I)
         sage: is_QuotientRing(S)
+        doctest:warning...
+        DeprecationWarning: The function is_QuotientRing is deprecated;
+        use 'isinstance(..., QuotientRing_nc)' instead.
+        See https://github.com/sagemath/sage/issues/38266 for details.
         True
         sage: is_QuotientRing(R)
         False
@@ -366,6 +370,10 @@ def is_QuotientRing(x):
         sage: is_QuotientRing(F)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38266,
+                "The function is_QuotientRing is deprecated; "
+                "use 'isinstance(..., QuotientRing_nc)' instead.")
     return isinstance(x, QuotientRing_nc)
 
 
diff --git a/src/sage/rings/valuation/augmented_valuation.py b/src/sage/rings/valuation/augmented_valuation.py
index 3d415c6e83c..de97c20fe0b 100644
--- a/src/sage/rings/valuation/augmented_valuation.py
+++ b/src/sage/rings/valuation/augmented_valuation.py
@@ -555,8 +555,8 @@ def extensions(self, ring):
         if ring is self.domain():
             return [self]
 
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if is_PolynomialRing(ring):  # univariate
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if isinstance(ring, PolynomialRing_general):  # univariate
             base_valuations = self._base_valuation.extensions(ring)
             phi = self.phi().change_ring(ring.base_ring())
 
@@ -595,8 +595,8 @@ def restriction(self, ring):
             base = self._base_valuation.restriction(ring)
             if ring.is_subring(self.domain().base_ring()):
                 return base
-            from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-            if is_PolynomialRing(ring):  # univariate
+            from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+            if isinstance(ring, PolynomialRing_general):  # univariate
                 return base.augmentation(self.phi().change_ring(ring.base_ring()), self._mu)
         return super().restriction(ring)
 
@@ -817,8 +817,8 @@ def change_domain(self, ring):
             [ Gauss valuation induced by 2-adic valuation, v(x) = 1 ]
 
         """
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if is_PolynomialRing(ring) and ring.variable_name() == self.domain().variable_name():
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if isinstance(ring, PolynomialRing_general) and ring.variable_name() == self.domain().variable_name():
             return self._base_valuation.change_domain(ring).augmentation(self.phi().change_ring(ring.base_ring()), self._mu, check=False)
         return super().change_domain(ring)
 
diff --git a/src/sage/rings/valuation/developing_valuation.py b/src/sage/rings/valuation/developing_valuation.py
index f99c2b5161c..5387ec8dda7 100644
--- a/src/sage/rings/valuation/developing_valuation.py
+++ b/src/sage/rings/valuation/developing_valuation.py
@@ -83,8 +83,8 @@ def __init__(self, parent, phi):
         DiscretePseudoValuation.__init__(self, parent)
 
         domain = parent.domain()
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if not is_PolynomialRing(domain) or not domain.ngens() == 1:
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if not isinstance(domain, PolynomialRing_general) or not domain.ngens() == 1:
             raise TypeError("domain must be a univariate polynomial ring but %r is not" % (domain,))
 
         phi = domain.coerce(phi)
diff --git a/src/sage/rings/valuation/gauss_valuation.py b/src/sage/rings/valuation/gauss_valuation.py
index 0443ba9c670..509fa0610ab 100644
--- a/src/sage/rings/valuation/gauss_valuation.py
+++ b/src/sage/rings/valuation/gauss_valuation.py
@@ -89,8 +89,8 @@ def create_key(self, domain, v=None):
             ValueError: the domain of v must be the base ring of domain but 2-adic valuation is not defined over Integer Ring but over Rational Field
 
         """
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if not is_PolynomialRing(domain):
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if not isinstance(domain, PolynomialRing_general):
             raise TypeError("GaussValuations can only be created over polynomial rings but %r is not a polynomial ring" % (domain,))
         if not domain.ngens() == 1:
             raise NotImplementedError("domain must be univariate but %r is not univariate" % (domain,))
@@ -527,8 +527,8 @@ def change_domain(self, ring):
             Gauss valuation induced by 2-adic valuation
 
         """
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if is_PolynomialRing(ring) and ring.ngens() == 1:
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if isinstance(ring, PolynomialRing_general) and ring.ngens() == 1:
             base_valuation = self._base_valuation.change_domain(ring.base_ring())
             return GaussValuation(self.domain().change_ring(ring.base_ring()), base_valuation)
         return super().change_domain(ring)
@@ -546,8 +546,8 @@ def extensions(self, ring):
             [Gauss valuation induced by 2-adic valuation]
 
         """
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if is_PolynomialRing(ring) and ring.ngens() == 1:
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if isinstance(ring, PolynomialRing_general) and ring.ngens() == 1:
             if self.domain().is_subring(ring):
                 return [GaussValuation(ring, w) for w in self._base_valuation.extensions(ring.base_ring())]
         return super().extensions(ring)
@@ -567,8 +567,8 @@ def restriction(self, ring):
         """
         if ring.is_subring(self.domain().base_ring()):
             return self._base_valuation.restriction(ring)
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if is_PolynomialRing(ring) and ring.ngens() == 1:
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if isinstance(ring, PolynomialRing_general) and ring.ngens() == 1:
             if ring.base().is_subring(self.domain().base()):
                 return GaussValuation(ring, self._base_valuation.restriction(ring.base()))
         return super().restriction(ring)
diff --git a/src/sage/rings/valuation/inductive_valuation.py b/src/sage/rings/valuation/inductive_valuation.py
index 40f405e1b21..017e808ab99 100644
--- a/src/sage/rings/valuation/inductive_valuation.py
+++ b/src/sage/rings/valuation/inductive_valuation.py
@@ -1700,8 +1700,8 @@ def change_domain(self, ring):
             2-adic valuation
 
         """
-        from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
-        if is_PolynomialQuotientRing(ring) and ring.base() is self.domain() and ring.modulus() == self.phi():
+        from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
+        if isinstance(ring, PolynomialQuotientRing_generic) and ring.base() is self.domain() and ring.modulus() == self.phi():
             return self.restriction(self.domain().base())._extensions_to_quotient(ring, approximants=[self])[0]
         return super().change_domain(ring)
 
diff --git a/src/sage/rings/valuation/limit_valuation.py b/src/sage/rings/valuation/limit_valuation.py
index 11b41cf9fed..acb3fc478e0 100644
--- a/src/sage/rings/valuation/limit_valuation.py
+++ b/src/sage/rings/valuation/limit_valuation.py
@@ -422,8 +422,8 @@ def extensions(self, ring):
         """
         if self.domain() is ring:
             return [self]
-        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-        if is_PolynomialRing(ring) and self.domain().base_ring().is_subring(ring.base_ring()):
+        from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+        if isinstance(ring, PolynomialRing_general) and self.domain().base_ring().is_subring(ring.base_ring()):
             if self.domain().base_ring().fraction_field() is ring.base_ring():
                 return [LimitValuation(self._initial_approximation.change_domain(ring),
                         self._G.change_ring(ring.base_ring()))]
@@ -681,8 +681,8 @@ def residue_ring(self):
             # the approximation ends in v(phi)=infty
             return R
         else:
-            from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-            assert (is_PolynomialRing(R))
+            from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+            assert (isinstance(R, PolynomialRing_general))
             return R.base_ring()
 
     def _ge_(self, other):
diff --git a/src/sage/rings/valuation/valuation_space.py b/src/sage/rings/valuation/valuation_space.py
index 3eb143a6d4b..25ebb581430 100644
--- a/src/sage/rings/valuation/valuation_space.py
+++ b/src/sage/rings/valuation/valuation_space.py
@@ -535,8 +535,8 @@ def residue_field(self):
             from sage.categories.fields import Fields
             if ret in Fields():
                 return ret
-            from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-            if is_PolynomialRing(ret):
+            from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+            if isinstance(ret, PolynomialRing_general):
                 from sage.rings.function_field.constructor import FunctionField
                 return FunctionField(ret.base_ring().fraction_field(), names=(ret.variable_name(),))
             return ret.fraction_field()
diff --git a/src/sage/schemes/affine/affine_space.py b/src/sage/schemes/affine/affine_space.py
index 889d9005ed6..2b297d0c672 100644
--- a/src/sage/schemes/affine/affine_space.py
+++ b/src/sage/schemes/affine/affine_space.py
@@ -15,8 +15,8 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import RationalField
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.categories.map import Map
 from sage.categories.fields import Fields
@@ -109,7 +109,7 @@ def AffineSpace(n, R=None, names=None, ambient_projective_space=None,
         ...
         NameError: variable names passed to AffineSpace conflict with names in ring
     """
-    if (is_MPolynomialRing(n) or is_PolynomialRing(n)) and R is None:
+    if (isinstance(n, MPolynomialRing_base) or isinstance(n, PolynomialRing_general)) and R is None:
         R = n
         if names is not None:
             # Check for the case that the user provided a variable name
diff --git a/src/sage/schemes/curves/constructor.py b/src/sage/schemes/curves/constructor.py
index 687a238fcfa..4514943ddfd 100644
--- a/src/sage/schemes/curves/constructor.py
+++ b/src/sage/schemes/curves/constructor.py
@@ -39,7 +39,7 @@
 from sage.categories.number_fields import NumberFields
 
 from sage.rings.polynomial.multi_polynomial import MPolynomial
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.rational_field import QQ
 
@@ -240,7 +240,7 @@ def Curve(F, A=None):
 
         if isinstance(F, (list, tuple)):
             P = Sequence(F).universe()
-            if not is_MPolynomialRing(P):
+            if not isinstance(P, MPolynomialRing_base):
                 raise TypeError("universe of F must be a multivariate polynomial ring")
             for f in F:
                 if not f.is_homogeneous():
diff --git a/src/sage/schemes/elliptic_curves/constructor.py b/src/sage/schemes/elliptic_curves/constructor.py
index 21470bd890a..ccbc004a8d3 100644
--- a/src/sage/schemes/elliptic_curves/constructor.py
+++ b/src/sage/schemes/elliptic_curves/constructor.py
@@ -28,7 +28,7 @@
 from sage.rings.rational_field import RationalField
 
 import sage.rings.abc
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
 from sage.rings.number_field.number_field_base import NumberField
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.multi_polynomial import MPolynomial
@@ -1098,7 +1098,7 @@ def EllipticCurve_from_cubic(F, P=None, morphism=True):
     # check the input
     R = F.parent()
     K = R.base_ring()
-    if not is_MPolynomialRing(R):
+    if not isinstance(R, MPolynomialRing_base):
         raise TypeError('equation must be a polynomial')
     if R.ngens() != 3 or F.nvariables() != 3:
         raise TypeError('equation must be a polynomial in three variables')
@@ -1333,7 +1333,7 @@ def chord_and_tangent(F, P):
     from sage.schemes.curves.constructor import Curve
     # check the input
     R = F.parent()
-    if not is_MPolynomialRing(R):
+    if not isinstance(R, MPolynomialRing_base):
         raise TypeError('equation must be a polynomial')
     if R.ngens() != 3:
         raise TypeError('{} is not a polynomial in three variables'.format(F))
diff --git a/src/sage/schemes/elliptic_curves/ell_local_data.py b/src/sage/schemes/elliptic_curves/ell_local_data.py
index f600259eef7..d0bbd858d44 100644
--- a/src/sage/schemes/elliptic_curves/ell_local_data.py
+++ b/src/sage/schemes/elliptic_curves/ell_local_data.py
@@ -102,7 +102,7 @@
 from sage.rings.number_field.number_field_ideal import NumberFieldFractionalIdeal
 
 from sage.rings.number_field.number_field_base import NumberField
-from sage.rings.ideal import is_Ideal
+from sage.rings.ideal import Ideal_generic
 
 from .constructor import EllipticCurve
 from .kodaira_symbol import KodairaSymbol
@@ -1185,7 +1185,7 @@ def check_prime(K, P):
                 raise TypeError("The element %s is not prime" % (P,))
         elif P in QQ:
             raise TypeError("The element %s is not prime" % (P,))
-        elif is_Ideal(P) and P.base_ring() is ZZ:
+        elif isinstance(P, Ideal_generic) and P.base_ring() is ZZ:
             if P.is_prime():
                 return P.gen()
             else:
diff --git a/src/sage/schemes/generic/algebraic_scheme.py b/src/sage/schemes/generic/algebraic_scheme.py
index 8cc0e544917..275379e1562 100644
--- a/src/sage/schemes/generic/algebraic_scheme.py
+++ b/src/sage/schemes/generic/algebraic_scheme.py
@@ -116,7 +116,7 @@
 
 from sage.categories.number_fields import NumberFields
 
-from sage.rings.ideal import is_Ideal
+from sage.rings.ideal import Ideal_generic
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import RationalField
 from sage.rings.finite_rings.finite_field_base import FiniteField
@@ -936,17 +936,17 @@ def __init__(self, A, polynomials, category=None):
             Closed subscheme of Projective Space of dimension 2 over Rational Field defined by:
               x^2 - y*z
         """
-        from sage.rings.polynomial.multi_polynomial_sequence import is_PolynomialSequence
+        from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence_generic
 
         AlgebraicScheme.__init__(self, A, category=category)
         self._base_ring = A.base_ring()
         R = A.coordinate_ring()
-        if is_Ideal(polynomials):
+        if isinstance(polynomials, Ideal_generic):
             I = polynomials
             polynomials = I.gens()
             if I.ring() is R: # Otherwise we will recompute I later after
                 self.__I = I  # converting generators to the correct ring
-        if isinstance(polynomials, tuple) or is_PolynomialSequence(polynomials) or is_iterator(polynomials):
+        if isinstance(polynomials, tuple) or isinstance(polynomials, PolynomialSequence_generic) or is_iterator(polynomials):
             polynomials = list(polynomials)
         elif not isinstance(polynomials, list):
             # Looks like we got a single polynomial
diff --git a/src/sage/schemes/generic/point.py b/src/sage/schemes/generic/point.py
index 7ef85645f56..e5695cca656 100644
--- a/src/sage/schemes/generic/point.py
+++ b/src/sage/schemes/generic/point.py
@@ -170,8 +170,8 @@ def __init__(self, S, P, check=False):
              the Ideal (-x^2 + y*z) of Multivariate Polynomial Ring in x, y, z over Rational Field
         """
         R = S.coordinate_ring()
-        from sage.rings.ideal import is_Ideal
-        if not is_Ideal(P):
+        from sage.rings.ideal import Ideal_generic
+        if not isinstance(P, Ideal_generic):
             P = R.ideal(P)
         elif P.ring() is not R:
             P = R.ideal(P.gens())
diff --git a/src/sage/schemes/generic/scheme.py b/src/sage/schemes/generic/scheme.py
index 715c9d2a687..c1c60256387 100644
--- a/src/sage/schemes/generic/scheme.py
+++ b/src/sage/schemes/generic/scheme.py
@@ -23,7 +23,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.rings.integer_ring import ZZ
 from sage.categories.commutative_rings import CommutativeRings
-from sage.rings.ideal import is_Ideal
+from sage.rings.ideal import Ideal_generic
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.schemes.generic.point import SchemeTopologicalPoint_prime_ideal
 
@@ -1016,7 +1016,7 @@ def __call__(self, *args):
         if len(args) == 1:
             x = args[0]
             if ((isinstance(x, self.element_class) and (x.parent() is self or x.parent() == self))
-                or (is_Ideal(x) and x.ring() is self.coordinate_ring())):
+                or (isinstance(x, Ideal_generic) and x.ring() is self.coordinate_ring())):
                 # Construct a topological point from x.
                 return self._element_constructor_(x)
         try:
@@ -1046,7 +1046,7 @@ def _element_constructor_(self, x):
                 return x
             elif x.parent() == self:
                 return self.element_class(self, x.prime_ideal())
-        elif is_Ideal(x) and x.ring() is self.coordinate_ring():
+        elif isinstance(x, Ideal_generic) and x.ring() is self.coordinate_ring():
             return self.element_class(self, x)
         raise TypeError('cannot convert %s to a topological point of %s' % (x, self))
 
diff --git a/src/sage/schemes/plane_conics/constructor.py b/src/sage/schemes/plane_conics/constructor.py
index 308b56f6db0..27cacbf72b0 100644
--- a/src/sage/schemes/plane_conics/constructor.py
+++ b/src/sage/schemes/plane_conics/constructor.py
@@ -32,8 +32,8 @@
 
 from sage.rings.number_field.number_field_base import NumberField
 from sage.rings.polynomial.multi_polynomial import MPolynomial
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.schemes.affine.affine_point import SchemeMorphism_point_affine
 from sage.schemes.projective.projective_point import SchemeMorphism_point_projective_field
@@ -242,7 +242,7 @@ def Conic(base_field, F=None, names=None, unique=True):
             return ProjectiveConic_rational_field(P2, F)
         if isinstance(base_field, NumberField):
             return ProjectiveConic_number_field(P2, F)
-        if isinstance(base_field, FractionField_generic) and (is_PolynomialRing(base_field.ring()) or is_MPolynomialRing(base_field.ring())):
+        if isinstance(base_field, FractionField_generic) and (isinstance(base_field.ring(), PolynomialRing_general) or isinstance(base_field.ring(), MPolynomialRing_base)):
             return ProjectiveConic_rational_function_field(P2, F)
 
         return ProjectiveConic_field(P2, F)
diff --git a/src/sage/schemes/projective/projective_space.py b/src/sage/schemes/projective/projective_space.py
index c05588f4698..529127850e5 100644
--- a/src/sage/schemes/projective/projective_space.py
+++ b/src/sage/schemes/projective/projective_space.py
@@ -85,8 +85,8 @@
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ, RationalField
 from sage.rings.fraction_field import FractionField
@@ -243,7 +243,7 @@ def ProjectiveSpace(n, R=None, names=None):
         sage: P.gens() == R.gens()
         True
     """
-    if (is_MPolynomialRing(n) or is_PolynomialRing(n)) and R is None:
+    if (isinstance(n, MPolynomialRing_base) or isinstance(n, PolynomialRing_general)) and R is None:
         if names is not None:
             # Check for the case that the user provided a variable name
             # That does not match what we wanted to use from R
diff --git a/src/sage/schemes/toric/fano_variety.py b/src/sage/schemes/toric/fano_variety.py
index c17cf7c37d7..ab7a7a2f4eb 100644
--- a/src/sage/schemes/toric/fano_variety.py
+++ b/src/sage/schemes/toric/fano_variety.py
@@ -128,8 +128,8 @@
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
 
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
+from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
 from sage.rings.fraction_field import FractionField_generic
 
 from sage.schemes.toric.toric_subscheme import AlgebraicScheme_subscheme_toric
@@ -1593,7 +1593,7 @@ def add_variables(field, variables):
     if isinstance(field, FractionField_generic):
         # Q(a) ---> Q(a, b) rather than Q(a)(b)
         R = field.ring()
-        if is_PolynomialRing(R) or is_MPolynomialRing(R):
+        if isinstance(R, PolynomialRing_general) or isinstance(R, MPolynomialRing_base):
             new_variables = list(R.variable_names())
             for v in variables:
                 if v not in new_variables:
diff --git a/src/sage/structure/element.pyx b/src/sage/structure/element.pyx
index a53c70a3f60..2b772465831 100644
--- a/src/sage/structure/element.pyx
+++ b/src/sage/structure/element.pyx
@@ -3208,8 +3208,8 @@ cdef class CommutativeRingElement(RingElement):
             sage: (x^2 + y^2 + z^2).mod( (x^3, y - z) )                                 # needs sage.libs.singular
             x^2 + 2*z^2
         """
-        from sage.rings.ideal import is_Ideal
-        if not is_Ideal(I) or not I.ring() is self._parent:
+        from sage.rings.ideal import Ideal_generic
+        if not isinstance(I, Ideal_generic) or not I.ring() is self._parent:
             I = self._parent.ideal(I)
             #raise TypeError, "I = %s must be an ideal in %s"%(I, self.parent())
         return I.reduce(self)
diff --git a/src/sage/structure/sequence.py b/src/sage/structure/sequence.py
index 0a4563d27e4..8abe231d8a3 100644
--- a/src/sage/structure/sequence.py
+++ b/src/sage/structure/sequence.py
@@ -256,12 +256,12 @@ def Sequence(x, universe=None, check=True, immutable=False, cr=False, cr_str=Non
     try:
         from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence
         from sage.rings.polynomial.pbori.pbori import BooleanMonomialMonoid
-        from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-        from sage.rings.quotient_ring import is_QuotientRing
+        from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
+        from sage.rings.quotient_ring import QuotientRing_nc
     except ImportError:
         pass
     else:
-        if is_MPolynomialRing(universe) or isinstance(universe, BooleanMonomialMonoid) or (is_QuotientRing(universe) and is_MPolynomialRing(universe.cover_ring())):
+        if isinstance(universe, MPolynomialRing_base) or isinstance(universe, BooleanMonomialMonoid) or (isinstance(universe, QuotientRing_nc) and isinstance(universe.cover_ring(), MPolynomialRing_base)):
             return PolynomialSequence(x, universe, immutable=immutable, cr=cr, cr_str=cr_str)
 
     return Sequence_generic(x, universe, check, immutable, cr, cr_str, use_sage_types)
diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
index a92fe241355..cb65cfe3b9a 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -7710,10 +7710,10 @@ cdef class Expression(Expression_abc):
             TypeError: y is not a variable of Multivariate Polynomial Ring in x over Ring of integers modulo 4
         """
         from sage.symbolic.ring import SR
-        from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+        from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
         base_ring = R.base_ring()
         if base_ring == SR:
-            if is_MPolynomialRing(R):
+            if isinstance(R, MPolynomialRing_base):
                 return R({tuple([0]*R.ngens()):self})
             else:
                 return R([self])
diff --git a/src/sage/symbolic/ring.pyx b/src/sage/symbolic/ring.pyx
index 501b0920898..324745d94aa 100644
--- a/src/sage/symbolic/ring.pyx
+++ b/src/sage/symbolic/ring.pyx
@@ -208,8 +208,8 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing):
             return False
         else:
             from sage.rings.fraction_field import FractionField_generic
-            from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-            from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+            from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
+            from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_base
             from sage.rings.polynomial.laurent_polynomial_ring_base import LaurentPolynomialRing_generic
             from sage.rings.infinity import InfinityRing, UnsignedInfinityRing
             from sage.rings.real_lazy import RLF, CLF
@@ -220,7 +220,7 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing):
             if R._is_numerical():
                 # Almost anything with a coercion into any precision of CC
                 return R not in (RLF, CLF)
-            elif is_PolynomialRing(R) or is_MPolynomialRing(R) or isinstance(R, FractionField_generic) or isinstance(R, LaurentPolynomialRing_generic):
+            elif isinstance(R, PolynomialRing_general) or isinstance(R, MPolynomialRing_base) or isinstance(R, FractionField_generic) or isinstance(R, LaurentPolynomialRing_generic):
                 base = R.base_ring()
                 return base is not self and self.has_coerce_map_from(base)
             elif (R is InfinityRing or R is UnsignedInfinityRing