diff --git a/src/sage/algebras/quatalg/quaternion_algebra.py b/src/sage/algebras/quatalg/quaternion_algebra.py
index 885ab854170..93e22abd6fd 100644
--- a/src/sage/algebras/quatalg/quaternion_algebra.py
+++ b/src/sage/algebras/quatalg/quaternion_algebra.py
@@ -51,7 +51,7 @@
 from sage.rings.rational import Rational
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.ideal import Ideal_fractional
-from sage.rings.rational_field import is_RationalField, QQ
+from sage.rings.rational_field import RationalField, QQ
 from sage.rings.infinity import infinity
 from sage.rings.number_field.number_field_base import NumberField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -429,7 +429,7 @@ def is_division_algebra(self) -> bool:
             ...
             NotImplementedError: base field must be rational numbers
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise NotImplementedError("base field must be rational numbers")
         return self.discriminant() != 1
 
@@ -453,7 +453,7 @@ def is_matrix_ring(self) -> bool:
             NotImplementedError: base field must be rational numbers
 
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise NotImplementedError("base field must be rational numbers")
         return self.discriminant() == 1
 
@@ -678,7 +678,7 @@ def __init__(self, base_ring, a, b, names='i,j,k'):
         Parent.__init__(self, base=base_ring, names=names, category=cat)
         self._a = a
         self._b = b
-        if is_RationalField(base_ring) and a.denominator() == 1 == b.denominator():
+        if isinstance(base_ring, RationalField) and a.denominator() == 1 == b.denominator():
             self.Element = QuaternionAlgebraElement_rational_field
         elif (isinstance(base_ring, NumberField) and base_ring.degree() > 2 and base_ring.is_absolute() and
               a.denominator() == 1 == b.denominator() and base_ring.defining_polynomial().is_monic()):
@@ -1066,7 +1066,7 @@ def is_definite(self):
             ...
             ValueError: base field must be rational numbers
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise ValueError("base field must be rational numbers")
         a, b = self.invariants()
         return a < 0 and b < 0
@@ -1218,7 +1218,7 @@ def discriminant(self):
             sage: QuaternionAlgebra(QQ[sqrt(2)], 3, 19).discriminant()                  # needs sage.symbolic
             Fractional ideal (1)
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             try:
                 F = self.base_ring()
                 return F.hilbert_conductor(self._a, self._b)
@@ -1245,7 +1245,7 @@ def ramified_primes(self):
             sage: QuaternionAlgebra(QQ, -58, -69).ramified_primes()
             [3, 23, 29]
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise ValueError("base field must be the rational numbers")
 
         a, b = self._a, self._b
@@ -2517,7 +2517,7 @@ def attempt_isomorphism(self, other):
         if other.quaternion_algebra() != Q:
             raise TypeError('not an order in the same quaternion algebra')
 
-        if not is_RationalField(Q.base_ring()):
+        if not isinstance(Q.base_ring(), RationalField):
             raise NotImplementedError('only implemented for orders in a rational quaternion algebra')
         if not Q.is_definite():
             raise NotImplementedError('only implemented for definite quaternion orders')
diff --git a/src/sage/combinat/finite_state_machine_generators.py b/src/sage/combinat/finite_state_machine_generators.py
index 11cd2d1b3ab..ae708a195ca 100644
--- a/src/sage/combinat/finite_state_machine_generators.py
+++ b/src/sage/combinat/finite_state_machine_generators.py
@@ -268,8 +268,8 @@ def Word(self, word, input_alphabet=None):
 
         TESTS::
 
-            sage: from sage.rings.integer import is_Integer
-            sage: all(is_Integer(s.label()) for s in A.states())
+            sage: from sage.rings.integer import Integer
+            sage: all(isinstance(s.label(), Integer) for s in A.states())
             True
         """
         letters = list(word)
diff --git a/src/sage/combinat/sf/jack.py b/src/sage/combinat/sf/jack.py
index 8c62cfb08df..e70959f8dfc 100644
--- a/src/sage/combinat/sf/jack.py
+++ b/src/sage/combinat/sf/jack.py
@@ -36,7 +36,7 @@
 from sage.rings.rational_field import QQ
 from sage.arith.misc import gcd
 from sage.arith.functions import lcm
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.misc.misc_c import prod
 from sage.categories.morphism import SetMorphism
 from sage.categories.homset import Hom, End
@@ -481,7 +481,7 @@ def normalize_coefficients(self, c):
         6/(t^2 + 3*t + 2)
     """
     BR = self.base_ring()
-    if is_FractionField(BR) and BR.base_ring() == QQ:
+    if isinstance(BR, FractionField_generic) and BR.base_ring() == QQ:
         denom = c.denominator()
         numer = c.numerator()
 
diff --git a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
index a1e4bc1700d..2b9dd28b13b 100644
--- a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
@@ -45,7 +45,7 @@ class initialization directly.
 from sage.rings.integer import Integer
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.fraction_field import FractionField
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.rings.quotient_ring import is_QuotientRing
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space_field
@@ -261,7 +261,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
             polys = [morphism_or_polys]
 
         PR = get_coercion_model().common_parent(*polys)
-        fraction_field = any(is_FractionField(poly.parent()) for poly in polys)
+        fraction_field = any(isinstance(poly.parent(), FractionField_generic) for poly in polys)
         if fraction_field:
             K = PR.base_ring().fraction_field()
             # Replace base ring with its fraction field
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
index 4b3ebd0d89a..a04cf57a28d 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
@@ -87,8 +87,8 @@ class initialization directly.
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.finite_rings.integer_mod_ring import Zmod
-from sage.rings.fraction_field import (FractionField, is_FractionField, FractionField_1poly_field)
-from sage.rings.fraction_field_element import is_FractionFieldElement, FractionFieldElement
+from sage.rings.fraction_field import FractionField, FractionField_generic, FractionField_1poly_field
+from sage.rings.fraction_field_element import FractionFieldElement
 from sage.rings.function_field.function_field import is_FunctionField
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
@@ -394,11 +394,11 @@ 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 is_FractionField(aff_CR)
+            if (not is_PolynomialRing(aff_CR) and not isinstance(aff_CR, FractionField_generic)
                 and not (is_MPolynomialRing(aff_CR) and aff_CR.ngens() == 1)):
                 msg = '{} is not a single variable polynomial or rational function'
                 raise ValueError(msg.format(f))
-            if is_FractionField(aff_CR):
+            if isinstance(aff_CR, FractionField_generic):
                 polys = [f.numerator(),f.denominator()]
             else:
                 polys = [f, aff_CR(1)]
@@ -889,7 +889,7 @@ def dynatomic_polynomial(self, period):
                         # do it again to divide out by denominators of coefficients
                         PHI = QR2[0].sage()
                         PHI = PHI.numerator()._maxima_().divide(PHI.denominator())[0].sage()
-                    if not is_FractionFieldElement(PHI):
+                    if not isinstance(PHI, FractionFieldElement):
                         from sage.symbolic.expression_conversions import polynomial
                         PHI = polynomial(PHI, ring=self.coordinate_ring())
                 except (TypeError, NotImplementedError): #something Maxima, or the conversion, can't handle
@@ -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 is_FractionField(R):
+                    if is_PolynomialRing(R) or is_MPolynomialRing(R) or isinstance(R, FractionField_generic):
                         # for polynomial rings, we can get an infinite family of hyperplanes
                         # by increasing the degree
                         var = R.gen()
@@ -3702,7 +3702,7 @@ def automorphism_group(self, **kwds):
             raise NotImplementedError("rational function of degree 1 not implemented")
         f = self.dehomogenize(1)
         R = PolynomialRing(f.base_ring(),'x')
-        if is_FractionFieldElement(f[0]):
+        if isinstance(f[0], FractionFieldElement):
             F = (f[0].numerator().univariate_polynomial(R))/f[0].denominator().univariate_polynomial(R)
         else:
             F = f[0].univariate_polynomial(R)
@@ -4880,7 +4880,7 @@ def periodic_points(self, n, minimal=True, formal=False, R=None, algorithm='vari
         if isinstance(R, FractionField_1poly_field) or is_FunctionField(R):
             raise NotImplementedError('periodic points not implemented for fraction function fields; '
                 'clear denominators and use the polynomial ring instead')
-        if is_FractionField(R):
+        if isinstance(R, FractionField_generic):
             if is_MPolynomialRing(R.ring()):
                 raise NotImplementedError('periodic points not implemented for fraction function fields; '
                     'clear denominators and use the polynomial ring instead')
@@ -5784,7 +5784,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
                     X = X.change_ring(F)
                 else:
                     F = base_ring
-                    if is_FractionField(base_ring):
+                    if isinstance(base_ring, FractionField_generic):
                         if is_MPolynomialRing(base_ring.ring()) or is_PolynomialRing(base_ring.ring()):
                             f.normalize_coordinates()
                             f_ring = f.change_ring(base_ring.ring())
@@ -5886,7 +5886,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
             return sigmas
 
         base_ring = dom.base_ring()
-        if is_FractionField(base_ring):
+        if isinstance(base_ring, FractionField_generic):
             base_ring = base_ring.ring()
         if (is_PolynomialRing(base_ring) or is_MPolynomialRing(base_ring)):
             base_ring = base_ring.base_ring()
diff --git a/src/sage/dynamics/complex_dynamics/mandel_julia.py b/src/sage/dynamics/complex_dynamics/mandel_julia.py
index 00eb7d473eb..8ceb38d0cec 100644
--- a/src/sage/dynamics/complex_dynamics/mandel_julia.py
+++ b/src/sage/dynamics/complex_dynamics/mandel_julia.py
@@ -51,7 +51,7 @@
 from sage.schemes.projective.projective_space import ProjectiveSpace
 from sage.misc.prandom import randint
 from sage.calculus.var import var
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.categories.function_fields import FunctionFields
 
 lazy_import('sage.dynamics.arithmetic_dynamics.generic_ds', 'DynamicalSystem')
@@ -243,14 +243,14 @@ def mandelbrot_plot(f=None, **kwds):
         P = f.parent()
 
         if P.base_ring() is CC or P.base_ring() is CDF:
-            if is_FractionField(P):
+            if isinstance(P, FractionField_generic):
                 raise NotImplementedError("coefficients must be polynomials in the parameter")
             gen_list = list(P.gens())
             parameter = gen_list.pop(gen_list.index(parameter))
             variable = gen_list.pop()
 
         elif P.base_ring().base_ring() is CC or P.base_ring().base_ring() is CDF:
-            if is_FractionField(P.base_ring()):
+            if isinstance(P.base_ring(), FractionField_generic):
                 raise NotImplementedError("coefficients must be polynomials in the parameter")
             phi = P.flattening_morphism()
             f = phi(f)
diff --git a/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx b/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx
index 2cb446886e1..479589dc0e3 100644
--- a/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx
+++ b/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx
@@ -34,7 +34,7 @@ from sage.ext.fast_callable import fast_callable
 from sage.calculus.all import symbolic_expression
 from sage.symbolic.ring import SR
 from sage.calculus.var import var
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.categories.function_fields import FunctionFields
 from cypari2.handle_error import PariError
 from math import sqrt
@@ -709,14 +709,14 @@ cpdef polynomial_mandelbrot(f, parameter=None, double x_center=0,
     P = f.parent()
 
     if P.base_ring() is CC:
-        if is_FractionField(P):
+        if isinstance(P, FractionField_generic):
             raise NotImplementedError("coefficients must be polynomials in the parameter")
         gen_list = list(P.gens())
         parameter = gen_list.pop(gen_list.index(parameter))
         variable = gen_list.pop()
 
     elif P.base_ring().base_ring() is CC:
-        if is_FractionField(P.base_ring()):
+        if isinstance(P.base_ring(), FractionField_generic):
             raise NotImplementedError("coefficients must be polynomials in the parameter")
         phi = P.flattening_morphism()
         f = phi(f)
diff --git a/src/sage/functions/transcendental.py b/src/sage/functions/transcendental.py
index 1c657f5b8b3..3dcb446e706 100644
--- a/src/sage/functions/transcendental.py
+++ b/src/sage/functions/transcendental.py
@@ -28,10 +28,10 @@
 
 lazy_import('sage.combinat.combinat', 'bernoulli_polynomial')
 lazy_import('sage.rings.cc', 'CC')
-lazy_import('sage.rings.complex_mpfr', ['ComplexField', 'is_ComplexNumber'])
+lazy_import('sage.rings.complex_mpfr', ['ComplexField', 'ComplexNumber'])
 lazy_import('sage.rings.polynomial.polynomial_real_mpfr_dense', 'PolynomialRealDense')
 lazy_import('sage.rings.real_double', 'RDF')
-lazy_import('sage.rings.real_mpfr', ['RR', 'RealField', 'is_RealNumber'])
+lazy_import('sage.rings.real_mpfr', ['RR', 'RealField', 'RealNumber'])
 
 lazy_import('sage.libs.mpmath.utils', 'call', as_='_mpmath_utils_call')
 lazy_import('mpmath', 'zeta', as_='_mpmath_zeta')
@@ -452,7 +452,7 @@ def zeta_symmetric(s):
     - I copied the definition of xi from
       http://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html
     """
-    if not (is_ComplexNumber(s) or is_RealNumber(s)):
+    if not (isinstance(s, ComplexNumber) or isinstance(s, RealNumber)):
         s = ComplexField()(s)
 
     R = s.parent()
@@ -544,7 +544,7 @@ def _eval_(self, x):
             sage: dickman_rho(0)                                                        # needs sage.symbolic
             1.00000000000000
         """
-        if not is_RealNumber(x):
+        if not isinstance(x, RealNumber):
             try:
                 x = RR(x)
             except (TypeError, ValueError):
diff --git a/src/sage/groups/affine_gps/affine_group.py b/src/sage/groups/affine_gps/affine_group.py
index 7d27488ec59..07b63d4a2bc 100644
--- a/src/sage/groups/affine_gps/affine_group.py
+++ b/src/sage/groups/affine_gps/affine_group.py
@@ -173,8 +173,8 @@ def __classcall__(cls, *args, **kwds):
             ring = V.base_ring()
         if len(args) == 2:
             degree, ring = args
-            from sage.rings.integer import is_Integer
-            if is_Integer(ring):
+            from sage.rings.integer import Integer
+            if isinstance(ring, Integer):
                 from sage.rings.finite_rings.finite_field_constructor import FiniteField
                 var = kwds.get('var', 'a')
                 ring = FiniteField(ring, var)
diff --git a/src/sage/groups/matrix_gps/matrix_group.py b/src/sage/groups/matrix_gps/matrix_group.py
index ef05b55c190..f9135822de4 100644
--- a/src/sage/groups/matrix_gps/matrix_group.py
+++ b/src/sage/groups/matrix_gps/matrix_group.py
@@ -59,7 +59,7 @@
 
 from sage.categories.groups import Groups
 from sage.categories.rings import Rings
-from sage.rings.integer import is_Integer
+from sage.rings.integer import Integer
 from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.latex import latex
 from sage.structure.richcmp import (richcmp_not_equal, rich_to_bool,
@@ -417,7 +417,7 @@ def __init__(self, degree, base_ring, category=None):
             True
         """
         assert base_ring in Rings
-        assert is_Integer(degree)
+        assert isinstance(degree, Integer)
 
         self._deg = degree
         if self._deg <= 0:
diff --git a/src/sage/matrix/matrix0.pyx b/src/sage/matrix/matrix0.pyx
index c5280bbe578..83edc74c16d 100644
--- a/src/sage/matrix/matrix0.pyx
+++ b/src/sage/matrix/matrix0.pyx
@@ -42,7 +42,7 @@ from sage.categories.commutative_rings import CommutativeRings
 from sage.categories.rings import Rings
 
 import sage.rings.abc
-from sage.rings.integer_ring import is_IntegerRing
+from sage.rings.integer_ring import IntegerRing_class
 
 import sage.modules.free_module
 
@@ -5975,7 +5975,7 @@ cdef class Matrix(sage.structure.element.Matrix):
                 return (~self.lift_centered()).change_ring(R)
             except (TypeError, ZeroDivisionError):
                 raise ZeroDivisionError("input matrix must be nonsingular")
-        elif algorithm is None and is_IntegerRing(R):
+        elif algorithm is None and isinstance(R, IntegerRing_class):
             try:
                 return (~self).change_ring(R)
             except (TypeError, ZeroDivisionError):
diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx
index c0f1d646340..af5058ae67c 100644
--- a/src/sage/matrix/matrix2.pyx
+++ b/src/sage/matrix/matrix2.pyx
@@ -93,8 +93,8 @@ from sage.structure.element import Vector
 from sage.structure.element cimport have_same_parent
 from sage.misc.verbose import verbose
 from sage.rings.number_field.number_field_base import NumberField
-from sage.rings.integer_ring import ZZ, is_IntegerRing
-from sage.rings.rational_field import QQ, is_RationalField
+from sage.rings.integer_ring import ZZ, IntegerRing_class
+from sage.rings.rational_field import QQ, RationalField
 import sage.rings.abc
 from sage.arith.numerical_approx cimport digits_to_bits
 
@@ -4538,11 +4538,11 @@ cdef class Matrix(Matrix1):
             algorithm = 'default'
         elif algorithm not in ['default', 'generic', 'flint', 'pari', 'padic', 'pluq']:
             raise ValueError("matrix kernel algorithm '%s' not recognized" % algorithm)
-        elif algorithm == 'padic' and not (is_IntegerRing(R) or is_RationalField(R)):
+        elif algorithm == 'padic' and not (isinstance(R, IntegerRing_class) or isinstance(R, RationalField)):
             raise ValueError("'padic' matrix kernel algorithm only available over the rationals and the integers, not over %s" % R)
-        elif algorithm == 'flint' and not (is_IntegerRing(R) or is_RationalField(R)):
+        elif algorithm == 'flint' and not (isinstance(R, IntegerRing_class) or isinstance(R, RationalField)):
             raise ValueError("'flint' matrix kernel algorithm only available over the rationals and the integers, not over %s" % R)
-        elif algorithm == 'pari' and not (is_IntegerRing(R) or (isinstance(R, NumberField) and not is_RationalField(R))):
+        elif algorithm == 'pari' and not (isinstance(R, IntegerRing_class) or (isinstance(R, NumberField) and not isinstance(R, RationalField))):
             raise ValueError("'pari' matrix kernel algorithm only available over non-trivial number fields and the integers, not over %s" % R)
         elif algorithm == 'generic' and R not in _Fields:
             raise ValueError("'generic' matrix kernel algorithm only available over a field, not over %s" % R)
@@ -4557,7 +4557,7 @@ cdef class Matrix(Matrix1):
             raise ValueError("matrix kernel basis format '%s' not recognized" % basis)
         elif basis == 'pivot' and R not in _Fields:
             raise ValueError('pivot basis only available over a field, not over %s' % R)
-        elif basis == 'LLL' and not is_IntegerRing(R):
+        elif basis == 'LLL' and not isinstance(R, IntegerRing_class):
             raise ValueError('LLL-reduced basis only available over the integers, not over %s' % R)
         if basis == 'default':
             basis = 'echelon' if R in _Fields else 'computed'
@@ -4566,7 +4566,7 @@ cdef class Matrix(Matrix1):
         proof = kwds.pop('proof', None)
         if proof not in [None, True, False]:
             raise ValueError("'proof' must be one of True, False or None, not %s" % proof)
-        if not (proof is None or is_IntegerRing(R)):
+        if not (proof is None or isinstance(R, IntegerRing_class)):
             raise ValueError("'proof' flag only valid for matrices over the integers")
 
         # We could sanitize/process remaining (un-popped) keywords here and
diff --git a/src/sage/matrix/matrix_rational_dense.pyx b/src/sage/matrix/matrix_rational_dense.pyx
index 27650a74482..60ef434904a 100644
--- a/src/sage/matrix/matrix_rational_dense.pyx
+++ b/src/sage/matrix/matrix_rational_dense.pyx
@@ -110,7 +110,7 @@ from sage.matrix.args cimport SparseEntry, MatrixArgs_init
 from sage.matrix.matrix_integer_dense cimport Matrix_integer_dense, _lift_crt
 from sage.structure.element cimport Element, Vector
 from sage.rings.integer cimport Integer
-from sage.rings.integer_ring import ZZ, is_IntegerRing
+from sage.rings.integer_ring import ZZ, IntegerRing_class
 import sage.rings.abc
 from sage.rings.rational_field import QQ
 
@@ -1465,7 +1465,7 @@ cdef class Matrix_rational_dense(Matrix_dense):
             if self._is_immutable:
                 return self
             return self.__copy__()
-        if is_IntegerRing(R):
+        if isinstance(R, IntegerRing_class):
             A, d = self._clear_denom()
             if not d.is_one():
                 raise TypeError("matrix has denominators so can't change to ZZ")
diff --git a/src/sage/matrix/matrix_space.py b/src/sage/matrix/matrix_space.py
index 473d961d090..71eb305c2be 100644
--- a/src/sage/matrix/matrix_space.py
+++ b/src/sage/matrix/matrix_space.py
@@ -402,7 +402,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
             if R.order() < matrix_modn_sparse.MAX_MODULUS:
                 return matrix_modn_sparse.Matrix_modn_sparse
 
-    if sage.rings.rational_field.is_RationalField(R):
+    if isinstance(R, sage.rings.rational_field.RationalField):
         try:
             from . import matrix_rational_sparse
         except ImportError:
@@ -410,7 +410,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
         else:
             return matrix_rational_sparse.Matrix_rational_sparse
 
-    if sage.rings.integer_ring.is_IntegerRing(R):
+    if isinstance(R, sage.rings.integer_ring.IntegerRing_class):
         try:
             from . import matrix_integer_sparse
         except ImportError:
diff --git a/src/sage/modular/dirichlet.py b/src/sage/modular/dirichlet.py
index 86b7a8a29f2..4d0436bad22 100644
--- a/src/sage/modular/dirichlet.py
+++ b/src/sage/modular/dirichlet.py
@@ -77,7 +77,7 @@
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.power_series_ring import PowerSeriesRing
-from sage.rings.rational_field import QQ, is_RationalField
+from sage.rings.rational_field import QQ, RationalField
 from sage.structure.element import MultiplicativeGroupElement
 from sage.structure.factory import UniqueFactory
 from sage.structure.gens_py import multiplicative_iterator
@@ -1386,7 +1386,7 @@ def gauss_sum(self, a=1):
         elif isinstance(K, sage.rings.abc.AlgebraicField):
             L = K
             zeta = L.zeta(m)
-        elif isinstance(K, sage.rings.abc.NumberField_cyclotomic) or is_RationalField(K):
+        elif isinstance(K, sage.rings.abc.NumberField_cyclotomic) or isinstance(K, RationalField):
             chi = chi.minimize_base_ring()
             n = lcm(m, G.zeta_order())
             L = CyclotomicField(n)
@@ -1467,7 +1467,7 @@ def phi(t):
             from sage.rings.complex_mpfr import ComplexField
             CC = ComplexField(prec)
             phi = CC.coerce_map_from(K)
-        elif isinstance(K, sage.rings.abc.NumberField_cyclotomic) or is_RationalField(K):
+        elif isinstance(K, sage.rings.abc.NumberField_cyclotomic) or isinstance(K, RationalField):
             phi = K.complex_embedding(prec)
             CC = phi.codomain()
         else:
@@ -1688,7 +1688,7 @@ def kloosterman_sum_numerical(self, prec=53, a=1, b=0):
         """
         G = self.parent()
         K = G.base_ring()
-        if not (isinstance(K, sage.rings.abc.NumberField_cyclotomic) or is_RationalField(K)):
+        if not (isinstance(K, sage.rings.abc.NumberField_cyclotomic) or isinstance(K, RationalField)):
             raise NotImplementedError("Kloosterman sums only currently implemented when the base ring is a cyclotomic field or QQ.")
         phi = K.complex_embedding(prec)
         CC = phi.codomain()
diff --git a/src/sage/modular/modform_hecketriangle/functors.py b/src/sage/modular/modform_hecketriangle/functors.py
index aae555d250a..b0fdfcf5ac7 100644
--- a/src/sage/modular/modform_hecketriangle/functors.py
+++ b/src/sage/modular/modform_hecketriangle/functors.py
@@ -78,12 +78,12 @@ def _get_base_ring(ring, var_name="d"):
         True
     """
 
-    # from sage.rings.fraction_field import is_FractionField
+    # from sage.rings.fraction_field import FractionField_generic
     from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
     from sage.categories.pushout import FractionField as FractionFieldFunctor
 
     base_ring = ring
-    # if (is_FractionField(base_ring)):
+    # if (isinstance(base_ring, FractionField_generic)):
     #    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/modular/modsym/relation_matrix.py b/src/sage/modular/modsym/relation_matrix.py
index ef0e17eef6a..7d58bb62a48 100644
--- a/src/sage/modular/modsym/relation_matrix.py
+++ b/src/sage/modular/modsym/relation_matrix.py
@@ -27,7 +27,7 @@
 from sage.misc.search import search
 from sage.misc.verbose import verbose
 from sage.modular.modsym.manin_symbol_list import ManinSymbolList
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.categories.rings import Rings
 
 
@@ -498,7 +498,7 @@ def relation_matrix_wtk_g0(syms, sign, field, sparse):
     rels = sorted(rels)
     # required for stability of doctests with python3
 
-    if syms._apply_S_only_0pm1() and is_RationalField(field):
+    if syms._apply_S_only_0pm1() and isinstance(field, RationalField):
         from . import relation_matrix_pyx
         mod = relation_matrix_pyx.sparse_2term_quotient_only_pm1(rels, len(syms))
     else:
diff --git a/src/sage/modules/free_module.py b/src/sage/modules/free_module.py
index ad94efcc94b..f1c7c7cdbaa 100644
--- a/src/sage/modules/free_module.py
+++ b/src/sage/modules/free_module.py
@@ -3823,7 +3823,7 @@ def index_in(self, other):
             return sage.rings.infinity.infinity
 
         a = sage.matrix.matrix_space.MatrixSpace(self.base_field(), self.rank())(C).determinant()
-        if sage.rings.integer_ring.is_IntegerRing(self.base_ring()):
+        if isinstance(self.base_ring(), sage.rings.integer_ring.IntegerRing_class):
             return a.abs()
         elif isinstance(self.base_ring, sage.rings.abc.Order):
             return self.base_ring().ideal(a).norm()
@@ -8266,10 +8266,10 @@ def element_class(R, is_sparse):
         <class 'sage.modules.free_module_element.FreeModuleElement_generic_dense'>
     """
     import sage.rings.integer_ring
-    if sage.rings.integer_ring.is_IntegerRing(R) and not is_sparse:
+    if isinstance(R, sage.rings.integer_ring.IntegerRing_class) and not is_sparse:
         from sage.modules.vector_integer_dense import Vector_integer_dense
         return Vector_integer_dense
-    elif sage.rings.rational_field.is_RationalField(R) and not is_sparse:
+    elif isinstance(R, sage.rings.rational_field.RationalField) and not is_sparse:
         from sage.modules.vector_rational_dense import Vector_rational_dense
         return Vector_rational_dense
     elif isinstance(R, sage.rings.abc.IntegerModRing) and not is_sparse:
diff --git a/src/sage/plot/plot3d/plot3d.py b/src/sage/plot/plot3d/plot3d.py
index ad885744ba7..4e19284828a 100644
--- a/src/sage/plot/plot3d/plot3d.py
+++ b/src/sage/plot/plot3d/plot3d.py
@@ -318,9 +318,9 @@ def to_cartesian(self, func, params=None):
 
         """
         from sage.structure.element import Expression
-        from sage.rings.real_mpfr import is_RealNumber
-        from sage.rings.integer import is_Integer
-        if params is not None and (isinstance(func, Expression) or is_RealNumber(func) or is_Integer(func)):
+        from sage.rings.real_mpfr import RealNumber
+        from sage.rings.integer import Integer
+        if params is not None and (isinstance(func, Expression) or isinstance(func, RealNumber) or isinstance(func, Integer)):
             return self.transform(**{
                 self.dep_var: func,
                 self.indep_vars[0]: params[0],
diff --git a/src/sage/probability/random_variable.py b/src/sage/probability/random_variable.py
index 4a385e55150..a07af1220d6 100644
--- a/src/sage/probability/random_variable.py
+++ b/src/sage/probability/random_variable.py
@@ -19,7 +19,7 @@
 from sage.structure.parent import Parent
 from sage.functions.log import log
 from sage.misc.functional import sqrt
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.sets.set import Set
 from pprint import pformat
 
@@ -343,11 +343,11 @@ def __init__(self, X, P, codomain=None, check=False):
         if codomain is None:
             from sage.rings.real_mpfr import RealField
             codomain = RealField()
-        if not isinstance(codomain, sage.rings.abc.RealField) and not is_RationalField(codomain):
+        if not isinstance(codomain, sage.rings.abc.RealField) and not isinstance(codomain, RationalField):
             raise TypeError("Argument codomain (= %s) must be the reals or rationals" % codomain)
         if check:
             one = sum(P.values())
-            if is_RationalField(codomain):
+            if isinstance(codomain, RationalField):
                 if not one == 1:
                     raise TypeError("Argument P (= %s) does not define a probability function")
             else:
diff --git a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
index 1039ce81bbc..f5163d394a5 100644
--- a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
+++ b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
@@ -3289,8 +3289,8 @@ def _coerce_map_from_(self, P):
             if self.base().has_coerce_map_from(P.base()):
                 return True
 
-        from sage.rings.fraction_field import is_FractionField
-        if is_FractionField(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
diff --git a/src/sage/rings/complex_double.pyx b/src/sage/rings/complex_double.pyx
index 2f85cbd101a..c59a2b46d6f 100644
--- a/src/sage/rings/complex_double.pyx
+++ b/src/sage/rings/complex_double.pyx
@@ -706,10 +706,18 @@ def is_ComplexDoubleElement(x):
 
         sage: from sage.rings.complex_double import is_ComplexDoubleElement
         sage: is_ComplexDoubleElement(0)
+        doctest:warning...
+        DeprecationWarning: The function is_ComplexDoubleElement is deprecated;
+        use 'isinstance(..., ComplexDoubleElement)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         False
         sage: is_ComplexDoubleElement(CDF(0))
         True
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_ComplexDoubleElement is deprecated; "
+                       "use 'isinstance(..., ComplexDoubleElement)' instead.")
     return isinstance(x, ComplexDoubleElement)
 
 
diff --git a/src/sage/rings/complex_interval.pyx b/src/sage/rings/complex_interval.pyx
index cd4ba7bb8e8..dd830421dd9 100644
--- a/src/sage/rings/complex_interval.pyx
+++ b/src/sage/rings/complex_interval.pyx
@@ -82,10 +82,18 @@ def is_ComplexIntervalFieldElement(x):
 
         sage: from sage.rings.complex_interval import is_ComplexIntervalFieldElement as is_CIFE
         sage: is_CIFE(CIF(2))
+        doctest:warning...
+        DeprecationWarning: The function is_ComplexIntervalFieldElement is deprecated;
+        use 'isinstance(..., ComplexIntervalFieldElement)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: is_CIFE(CC(2))
         False
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_ComplexIntervalFieldElement is deprecated; "
+                       "use 'isinstance(..., ComplexIntervalFieldElement)' instead.")
     return isinstance(x, ComplexIntervalFieldElement)
 
 
diff --git a/src/sage/rings/complex_mpfr.pyx b/src/sage/rings/complex_mpfr.pyx
index e1ce333d57d..79c06af06d5 100644
--- a/src/sage/rings/complex_mpfr.pyx
+++ b/src/sage/rings/complex_mpfr.pyx
@@ -127,6 +127,10 @@ def is_ComplexNumber(x):
         sage: a = ComplexNumber(1, 2); a
         1.00000000000000 + 2.00000000000000*I
         sage: is_ComplexNumber(a)
+        doctest:warning...
+        DeprecationWarning: The function is_ComplexNumber is deprecated;
+        use 'isinstance(..., ComplexNumber)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: b = ComplexNumber(1); b
         1.00000000000000
@@ -146,6 +150,10 @@ def is_ComplexNumber(x):
         sage: is_ComplexNumber(d)
         True
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_ComplexNumber is deprecated; "
+                       "use 'isinstance(..., ComplexNumber)' instead.")
     return isinstance(x, ComplexNumber)
 
 
diff --git a/src/sage/rings/finite_rings/element_givaro.pyx b/src/sage/rings/finite_rings/element_givaro.pyx
index a4a0aa5cd68..401f398ddee 100644
--- a/src/sage/rings/finite_rings/element_givaro.pyx
+++ b/src/sage/rings/finite_rings/element_givaro.pyx
@@ -69,7 +69,7 @@ from sage.structure.element cimport Vector
 
 from sage.interfaces.abc import GapElement
 
-cdef object is_IntegerMod
+cdef object IntegerMod_abstract
 cdef object Integer
 cdef object Rational
 cdef object MPolynomial
@@ -80,17 +80,17 @@ cdef void late_import() noexcept:
     """
     Late import of modules
     """
-    global is_IntegerMod, \
+    global IntegerMod_abstract, \
            Integer, \
            Rational, \
            MPolynomial, \
            Polynomial
 
-    if is_IntegerMod is not None:
+    if IntegerMod_abstract is not None:
         return
 
     import sage.rings.finite_rings.integer_mod
-    is_IntegerMod = sage.rings.finite_rings.integer_mod.is_IntegerMod
+    IntegerMod_abstract = sage.rings.finite_rings.integer_mod.IntegerMod_abstract
 
     import sage.rings.integer
     Integer = sage.rings.integer.Integer
@@ -361,7 +361,7 @@ cdef class Cache_givaro(Cache_base):
             else:
                 raise TypeError("unable to coerce from a finite field other than the prime subfield")
 
-        elif isinstance(e, (int, Integer)) or is_IntegerMod(e):
+        elif isinstance(e, (int, Integer)) or isinstance(e, IntegerMod_abstract):
             try:
                 e_int = e % self.characteristic()
                 self.objectptr.initi(res, e_int)
diff --git a/src/sage/rings/finite_rings/element_ntl_gf2e.pyx b/src/sage/rings/finite_rings/element_ntl_gf2e.pyx
index 512ac4ec1d2..32ffd192353 100644
--- a/src/sage/rings/finite_rings/element_ntl_gf2e.pyx
+++ b/src/sage/rings/finite_rings/element_ntl_gf2e.pyx
@@ -50,7 +50,7 @@ from sage.rings.finite_rings.finite_field_ntl_gf2e import FiniteField_ntl_gf2e
 from sage.interfaces.abc import GapElement
 
 
-cdef object is_IntegerMod
+cdef object IntegerMod_abstract
 cdef object Integer
 cdef object Rational
 cdef object MPolynomial
@@ -64,7 +64,7 @@ cdef int late_import() except -1:
     i.e. after the module was loaded. This is needed to avoid circular
     imports.
     """
-    global is_IntegerMod, \
+    global IntegerMod_abstract, \
            Integer, \
            Rational, \
            MPolynomial, \
@@ -72,11 +72,11 @@ cdef int late_import() except -1:
            GF, \
            GF2, GF2_0, GF2_1
 
-    if is_IntegerMod is not None:
+    if IntegerMod_abstract is not None:
         return 0
 
     import sage.rings.finite_rings.integer_mod
-    is_IntegerMod = sage.rings.finite_rings.integer_mod.is_IntegerMod
+    IntegerMod_abstract = sage.rings.finite_rings.integer_mod.IntegerMod_abstract
 
     import sage.rings.rational
     Rational = sage.rings.rational.Rational
@@ -275,7 +275,7 @@ cdef class Cache_ntl_gf2e(Cache_base):
         cdef FiniteField_ntl_gf2eElement g
         cdef Py_ssize_t i
 
-        if is_IntegerMod(e):
+        if isinstance(e, IntegerMod_abstract):
             e = e.lift()
         if isinstance(e, (int, Integer)):
             GF2E_conv_long(res.x,int(e&1))
diff --git a/src/sage/rings/finite_rings/integer_mod.pyx b/src/sage/rings/finite_rings/integer_mod.pyx
index 097f8ac87d3..b2238689afb 100644
--- a/src/sage/rings/finite_rings/integer_mod.pyx
+++ b/src/sage/rings/finite_rings/integer_mod.pyx
@@ -213,10 +213,18 @@ def is_IntegerMod(x):
 
         sage: from sage.rings.finite_rings.integer_mod import is_IntegerMod
         sage: is_IntegerMod(5)
+        doctest:warning...
+        DeprecationWarning: The function is_IntegerMod is deprecated;
+        use 'isinstance(..., IntegerMod_abstract)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         False
         sage: is_IntegerMod(Mod(5,10))
         True
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_IntegerMod is deprecated; "
+                       "use 'isinstance(..., IntegerMod_abstract)' instead.")
     return isinstance(x, IntegerMod_abstract)
 
 
@@ -4213,18 +4221,18 @@ def lucas(k, P, Q=1, n=None):
     """
     cdef IntegerMod_abstract p,q
 
-    if n is None and not is_IntegerMod(P):
+    if n is None and not isinstance(P, IntegerMod_abstract):
         raise ValueError
 
     if n is None:
         n = P.modulus()
 
-    if not is_IntegerMod(P):
+    if not isinstance(P, IntegerMod_abstract):
         p = Mod(P,n)
     else:
         p = P
 
-    if not is_IntegerMod(Q):
+    if not isinstance(Q, IntegerMod_abstract):
         q = Mod(Q,n)
     else:
         q = Q
diff --git a/src/sage/rings/finite_rings/residue_field.pyx b/src/sage/rings/finite_rings/residue_field.pyx
index 5e9d74844e3..7a7fa6dfc23 100644
--- a/src/sage/rings/finite_rings/residue_field.pyx
+++ b/src/sage/rings/finite_rings/residue_field.pyx
@@ -186,7 +186,7 @@ from sage.rings.ideal import is_Ideal
 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 is_FractionField
+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
@@ -1138,7 +1138,7 @@ cdef class ReductionMap(Map):
                 return FiniteField_prime_modn._element_constructor_(self._F, x)
             except ZeroDivisionError:
                 raise ZeroDivisionError("Cannot reduce rational %s modulo %s: it has negative valuation" % (x, p.gen()))
-        elif is_FractionField(self._K):
+        elif isinstance(self._K, FractionField_generic):
             p = p.gen()
             if p.degree() == 1:
                 return self._F((x.numerator() % p)[0] / (x.denominator() % p)[0])
@@ -1656,7 +1656,7 @@ cdef class LiftingMap(Section):
         """
         if self._K is QQ or self._K is ZZ:
             return self._K(x.lift())  # x.lift() is in ZZ
-        elif is_FractionField(self._K):
+        elif isinstance(self._K, FractionField_generic):
             if self._F.p.degree() == 1:
                 return self._K(self._K.ring_of_integers()(x))
             else:
diff --git a/src/sage/rings/fraction_field.py b/src/sage/rings/fraction_field.py
index 742729981eb..756cbbc9efc 100644
--- a/src/sage/rings/fraction_field.py
+++ b/src/sage/rings/fraction_field.py
@@ -151,10 +151,18 @@ def is_FractionField(x) -> bool:
 
         sage: from sage.rings.fraction_field import is_FractionField
         sage: is_FractionField(Frac(ZZ['x']))
+        doctest:warning...
+        DeprecationWarning: The function is_FractionField is deprecated;
+        use 'isinstance(..., FractionField_generic)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: is_FractionField(QQ)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38128,
+                "The function is_FractionField is deprecated; "
+                "use 'isinstance(..., FractionField_generic)' instead.")
     return isinstance(x, FractionField_generic)
 
 
diff --git a/src/sage/rings/fraction_field_element.pyx b/src/sage/rings/fraction_field_element.pyx
index a9c427c03bc..e651a0bf560 100644
--- a/src/sage/rings/fraction_field_element.pyx
+++ b/src/sage/rings/fraction_field_element.pyx
@@ -37,12 +37,20 @@ def is_FractionFieldElement(x):
         sage: from sage.rings.fraction_field_element import is_FractionFieldElement
         sage: R.<x> = ZZ[]
         sage: is_FractionFieldElement(x/2)
+        doctest:warning...
+        DeprecationWarning: The function is_FractionFieldElement is deprecated;
+        use 'isinstance(..., FractionFieldElement)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         False
         sage: is_FractionFieldElement(2/x)
         True
         sage: is_FractionFieldElement(1/3)
         False
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_FractionFieldElement is deprecated; "
+                       "use 'isinstance(..., FractionFieldElement)' instead.")
     return isinstance(x, FractionFieldElement)
 
 
diff --git a/src/sage/rings/integer.pyx b/src/sage/rings/integer.pyx
index 6d9155b643f..b4a1fa5039b 100644
--- a/src/sage/rings/integer.pyx
+++ b/src/sage/rings/integer.pyx
@@ -326,6 +326,10 @@ def is_Integer(x):
 
         sage: from sage.rings.integer import is_Integer
         sage: is_Integer(2)
+        doctest:warning...
+        DeprecationWarning: The function is_Integer is deprecated;
+        use 'isinstance(..., Integer)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: is_Integer(2/1)
         False
@@ -334,6 +338,10 @@ def is_Integer(x):
         sage: is_Integer('5')
         False
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_Integer is deprecated; "
+                       "use 'isinstance(..., Integer)' instead.")
     return isinstance(x, Integer)
 
 
diff --git a/src/sage/rings/integer_ring.pyx b/src/sage/rings/integer_ring.pyx
index 12b522a8bd7..a1574d00756 100644
--- a/src/sage/rings/integer_ring.pyx
+++ b/src/sage/rings/integer_ring.pyx
@@ -96,6 +96,10 @@ def is_IntegerRing(x):
 
         sage: from sage.rings.integer_ring import is_IntegerRing
         sage: is_IntegerRing(ZZ)
+        doctest:warning...
+        DeprecationWarning: The function is_IntegerRing is deprecated;
+        use 'isinstance(..., IntegerRing_class)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: is_IntegerRing(QQ)
         False
@@ -104,6 +108,10 @@ def is_IntegerRing(x):
         sage: is_IntegerRing(parent(1/3))
         False
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_IntegerRing is deprecated; "
+                       "use 'isinstance(..., IntegerRing_class)' instead.")
     return isinstance(x, IntegerRing_class)
 
 
diff --git a/src/sage/rings/laurent_series_ring.py b/src/sage/rings/laurent_series_ring.py
index 8df962fe320..e2b03bcca58 100644
--- a/src/sage/rings/laurent_series_ring.py
+++ b/src/sage/rings/laurent_series_ring.py
@@ -503,7 +503,7 @@ def _element_constructor_(self, x, n=0, prec=infinity):
             sage: P({-3: 1})
             x^-3
         """
-        from sage.rings.fraction_field_element import is_FractionFieldElement
+        from sage.rings.fraction_field_element import FractionFieldElement
         from sage.rings.lazy_series import LazyPowerSeries, LazyLaurentSeries
         from sage.rings.polynomial.multi_polynomial import MPolynomial
         from sage.rings.polynomial.polynomial_element import Polynomial
@@ -536,7 +536,7 @@ def _element_constructor_(self, x, n=0, prec=infinity):
                 return (x << n).add_bigoh(bigoh)
             else:  # General case, pretend to be a polynomial
                 return (self(self.polynomial_ring()(x)) << n).add_bigoh(prec)
-        elif (is_FractionFieldElement(x)
+        elif (isinstance(x, FractionFieldElement)
               and (x.base_ring() is self.base_ring() or x.base_ring() == self.base_ring())
               and isinstance(x.numerator(), (Polynomial, MPolynomial))):
             x = self(x.numerator()) / self(x.denominator())
diff --git a/src/sage/rings/number_field/splitting_field.py b/src/sage/rings/number_field/splitting_field.py
index ef26176664a..7fefcd02ce5 100644
--- a/src/sage/rings/number_field/splitting_field.py
+++ b/src/sage/rings/number_field/splitting_field.py
@@ -21,7 +21,7 @@
 from sage.arith.misc import factorial
 from sage.rings.number_field.number_field import NumberField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.rational_field import RationalField, is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.libs.pari.all import pari, PariError
 
 
@@ -382,7 +382,7 @@ def splitting_field(poly, name, map=False, degree_multiple=None, abort_degree=No
 
     # Kpol = PARI polynomial in y defining the extension found so far
     F = poly.base_ring()
-    if is_RationalField(F):
+    if isinstance(F, RationalField):
         Kpol = pari("'y")
     else:
         Kpol = F.pari_polynomial("y")
diff --git a/src/sage/rings/padics/common_conversion.pyx b/src/sage/rings/padics/common_conversion.pyx
index 0afddcc30a4..2a143e6d99e 100644
--- a/src/sage/rings/padics/common_conversion.pyx
+++ b/src/sage/rings/padics/common_conversion.pyx
@@ -148,7 +148,7 @@ cdef long get_ordp(x, PowComputer_class prime_pow) except? -10000:
             k = valp(pari_tmp)
         else: # t_INT and t_FRAC were converted before this function
             raise TypeError("unsupported coercion from pari: only p-adics, integers and rationals allowed")
-    elif sage.rings.finite_rings.integer_mod.is_IntegerMod(x):
+    elif isinstance(x, sage.rings.finite_rings.integer_mod.IntegerMod_abstract):
         value = <Integer>x.lift()
         if mpz_sgn(value.value) == 0:
             return maxordp
@@ -221,7 +221,7 @@ cdef long get_preccap(x, PowComputer_class prime_pow) except? -10000:
         pari_tmp = (<pari_gen>x).g
         # since get_ordp has been called typ(x.g) == t_PADIC
         k = valp(pari_tmp) + precp(pari_tmp)
-    elif sage.rings.finite_rings.integer_mod.is_IntegerMod(x):
+    elif isinstance(x, sage.rings.finite_rings.integer_mod.IntegerMod_abstract):
         k = mpz_remove(temp.value, (<Integer>x.modulus()).value, prime_pow.prime.value)
         if mpz_cmp_ui(temp.value, 1) != 0:
             raise TypeError("cannot coerce from the given integer mod ring (not a power of the same prime)")
@@ -411,7 +411,7 @@ cdef inline int cconv_shared(mpz_t out, x, long prec, long valshift, PowComputer
         x = x.sage()
     if isinstance(x, pAdicGenericElement) and x.parent().is_relaxed():
         x = x.lift(valshift + prec)
-    elif isinstance(x, pAdicGenericElement) or sage.rings.finite_rings.integer_mod.is_IntegerMod(x):
+    elif isinstance(x, pAdicGenericElement) or isinstance(x, sage.rings.finite_rings.integer_mod.IntegerMod_abstract):
         x = x.lift()
     if isinstance(x, Integer):
         if valshift > 0:
diff --git a/src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx b/src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx
index f10738d25d1..09062475876 100644
--- a/src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx
+++ b/src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx
@@ -185,7 +185,7 @@ from sage.libs.ntl.ntl_ZZ_pContext cimport ntl_ZZ_pContext_class
 from sage.rings.padics.padic_generic_element cimport pAdicGenericElement
 from sage.libs.pari.all import pari_gen
 from sage.interfaces.abc import GpElement
-from sage.rings.finite_rings.integer_mod import is_IntegerMod
+from sage.rings.finite_rings.integer_mod import IntegerMod_abstract
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
 from sage.rings.padics.padic_ext_element cimport pAdicExtElement
 from sage.rings.padics.precision_error import PrecisionError
@@ -339,7 +339,7 @@ cdef class pAdicZZpXCAElement(pAdicZZpXElement):
                 x = L
             else:
                 raise TypeError("unsupported coercion from pari: only p-adics, integers, rationals, polynomials and pol_mods allowed")
-        elif is_IntegerMod(x):
+        elif isinstance(x, IntegerMod_abstract):
             mpz_init(tmp)
             ctx_prec = mpz_remove(tmp, (<Integer>x.modulus()).value, self.prime_pow.prime.value)
             if mpz_cmp_ui(tmp, 1) == 0:
diff --git a/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx b/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx
index 8c29fa3ee73..3081c3f3d7a 100644
--- a/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx
+++ b/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx
@@ -203,7 +203,7 @@ from sage.libs.ntl.ntl_ZZ_pContext cimport ntl_ZZ_pContext_class
 from sage.rings.padics.padic_generic_element cimport pAdicGenericElement
 from sage.libs.pari.all import pari_gen
 from sage.interfaces.abc import GpElement
-from sage.rings.finite_rings.integer_mod import is_IntegerMod
+from sage.rings.finite_rings.integer_mod import IntegerMod_abstract
 from sage.rings.padics.padic_ext_element cimport pAdicExtElement
 from sage.rings.padics.precision_error import PrecisionError
 
@@ -354,7 +354,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement):
                 x = L
             else:
                 raise TypeError("unsupported coercion from pari: only p-adics, integers, rationals, polynomials and pol_mods allowed")
-        elif is_IntegerMod(x):
+        elif isinstance(x, IntegerMod_abstract):
             mpz_init(tmp)
             ctx_prec = mpz_remove(tmp, (<Integer>x.modulus()).value, self.prime_pow.prime.value)
             if mpz_cmp_ui(tmp, 1) == 0:
diff --git a/src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx b/src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx
index 44d549847a9..f85c6b7f3b4 100644
--- a/src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx
+++ b/src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx
@@ -145,7 +145,7 @@ from sage.libs.ntl.ntl_ZZ_pContext cimport ntl_ZZ_pContext_class
 from sage.rings.rational cimport Rational
 from sage.libs.pari.all import pari_gen
 from sage.interfaces.abc import GpElement
-from sage.rings.finite_rings.integer_mod import is_IntegerMod
+from sage.rings.finite_rings.integer_mod import IntegerMod_abstract
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
 
 
@@ -233,7 +233,7 @@ cdef class pAdicZZpXFMElement(pAdicZZpXElement):
                 x = L
             else:
                 raise TypeError("unsupported coercion from pari: only p-adics, integers, rationals, polynomials and pol_mods allowed")
-        elif is_IntegerMod(x):
+        elif isinstance(x, IntegerMod_abstract):
             if (<Integer>x.modulus())._is_power_of(<Integer>parent.prime()):
                 x = x.lift()
             else:
diff --git a/src/sage/rings/padics/padic_ZZ_pX_element.pyx b/src/sage/rings/padics/padic_ZZ_pX_element.pyx
index bf892956a16..f6ed8fe4706 100644
--- a/src/sage/rings/padics/padic_ZZ_pX_element.pyx
+++ b/src/sage/rings/padics/padic_ZZ_pX_element.pyx
@@ -41,7 +41,7 @@ from sage.libs.ntl.ntl_ZZ_pContext import ntl_ZZ_pContext
 from sage.rings.integer cimport Integer
 from sage.rings.rational cimport Rational
 from sage.rings.padics.padic_generic_element cimport pAdicGenericElement
-from sage.rings.finite_rings.integer_mod import is_IntegerMod
+from sage.rings.finite_rings.integer_mod import IntegerMod_abstract
 from sage.rings.padics.padic_printing cimport pAdicPrinter_class
 from sage.rings.padics.pow_computer_ext cimport PowComputer_ext
 from sage.rings.rational_field import QQ
@@ -664,7 +664,7 @@ cdef preprocess_list(pAdicZZpXElement elt, L):
                 L[i] = ntl_ZZ_p(L[i]*pshift_m, ctx)
             elif isinstance(L[i], pAdicGenericElement) and L[i]._is_base_elt(elt.prime_pow.prime):
                 L[i] = ntl_ZZ_p((L[i] >> min_val).lift(), ctx)
-            elif is_IntegerMod(L[i]):
+            elif isinstance(L[i], IntegerMod_abstract):
                 L[i] = ntl_ZZ_p(L[i].lift()*pshift_m, ctx)
             elif (L[i].modulus_context() is not ctx) or min_val != zero:
                 L[i] = ntl_ZZ_p(L[i].lift()*pshift_z, ctx)
@@ -682,7 +682,7 @@ cdef preprocess_list(pAdicZZpXElement elt, L):
                 L[i] = ntl_ZZ_p(L[i]//pshift_m, ctx)
             elif isinstance(L[i], pAdicGenericElement) and L[i]._is_base_elt(elt.prime_pow.prime):
                 L[i] = ntl_ZZ_p((L[i] >> min_val).lift(), ctx)
-            elif is_IntegerMod(L[i]):
+            elif isinstance(L[i], IntegerMod_abstract):
                 L[i] = ntl_ZZ_p(L[i].lift()//pshift_m, ctx)
             elif (L[i].modulus_context() is not ctx) or min_val != zero:
                 ZZ_div(tmp, (<ntl_ZZ>L[i].lift()).x, pshift_z.x)
@@ -693,7 +693,7 @@ cdef preprocess_list(pAdicZZpXElement elt, L):
         for i from 0 <= i < len(L):
             if isinstance(L[i], (ntl_ZZ, Integer, Rational, int)):
                 L[i] = ntl_ZZ_p(L[i], ctx)
-            elif (isinstance(L[i], pAdicGenericElement) and L[i]._is_base_elt(elt.prime_pow.prime)) or is_IntegerMod(L[i]) or (L[i].modulus_context() is not ctx):
+            elif (isinstance(L[i], pAdicGenericElement) and L[i]._is_base_elt(elt.prime_pow.prime)) or isinstance(L[i], IntegerMod_abstract) or (L[i].modulus_context() is not ctx):
                 L[i] = ntl_ZZ_p(L[i].lift(), ctx)
     return L, min_val, ctx
 
@@ -889,7 +889,7 @@ cdef get_val_prec(PowComputer_ext pp, a):
     cdef mpz_t leftover
     cdef long long_val
     cdef Integer Integer_val
-    if is_IntegerMod(a):
+    if isinstance(a, IntegerMod_abstract):
         mpz_init(leftover)
         long_val = mpz_remove(leftover, (<Integer>a.modulus()).value, pp.prime.value)
         if long_val > 0 and mpz_cmp_ui(leftover, 1) == 0:
diff --git a/src/sage/rings/padics/padic_template_element.pxi b/src/sage/rings/padics/padic_template_element.pxi
index 4b5b9c6dbe9..a3b203845b5 100644
--- a/src/sage/rings/padics/padic_template_element.pxi
+++ b/src/sage/rings/padics/padic_template_element.pxi
@@ -145,7 +145,7 @@ cdef class pAdicTemplateElement(pAdicGenericElement):
                         x = []
                     else:
                         x = [x]
-        elif sage.rings.finite_rings.integer_mod.is_IntegerMod(x):
+        elif isinstance(x, sage.rings.finite_rings.integer_mod.IntegerMod_abstract):
             if not Integer(self.prime_pow.prime).divides(x.parent().order()):
                 raise TypeError("p does not divide modulus %s" % x.parent().order())
         elif isinstance(x, Element) and isinstance(x.parent(), FiniteField):
diff --git a/src/sage/rings/polynomial/flatten.py b/src/sage/rings/polynomial/flatten.py
index 64ab7ed99d5..ef71d2b13a6 100644
--- a/src/sage/rings/polynomial/flatten.py
+++ b/src/sage/rings/polynomial/flatten.py
@@ -40,7 +40,7 @@
 from .polynomial_ring_constructor import PolynomialRing
 from .polynomial_ring import is_PolynomialRing
 from .multi_polynomial_ring_base import is_MPolynomialRing
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.rings.fraction_field_element import FractionFieldElement
 from sage.rings.polynomial.polydict import ETuple
 
@@ -538,8 +538,8 @@ def __init__(self, domain, D):
         # Construct unflattened codomain R
         new_vars = []
         R = domain
-        while is_PolynomialRing(R) or is_MPolynomialRing(R) or is_FractionField(R):
-            if is_FractionField(R):
+        while is_PolynomialRing(R) or is_MPolynomialRing(R) 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()
                 applicable_vars = {key: val for key, val in D.items()
@@ -679,7 +679,7 @@ def __init__(self, domain, D):
               To:   Fraction Field of Multivariate Polynomial Ring in x, y
                     over Univariate Polynomial Ring in a over Rational Field
         """
-        if not is_FractionField(domain):
+        if not isinstance(domain, FractionField_generic):
             raise TypeError("domain must be a fraction field")
         self._specialization = SpecializationMorphism(domain.base(), D)
         self._repr_type_str = 'Fraction Specialization'
diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
index cc31da00b9f..6b838190c52 100644
--- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
@@ -226,7 +226,7 @@ import sage.structure.element
 
 from sage.rings.rational cimport Rational
 from sage.rings.rational_field import QQ
-from sage.rings.integer_ring import is_IntegerRing, ZZ
+from sage.rings.integer_ring import IntegerRing_class, ZZ
 from sage.rings.integer cimport Integer
 from sage.rings.number_field.number_field_base cimport NumberField
 
@@ -5489,7 +5489,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
         if n_GetChar(_ring.cf) > 1<<29:
             raise NotImplementedError("Resultants of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.")
 
-        if is_IntegerRing(self._parent._base):
+        if isinstance(self._parent._base, IntegerRing_class):
             ret = self.change_ring(QQ).resultant(other.change_ring(QQ),
                                                  variable.change_ring(QQ))
             return ret.change_ring(ZZ)
diff --git a/src/sage/rings/polynomial/padics/polynomial_padic_flat.py b/src/sage/rings/polynomial/padics/polynomial_padic_flat.py
index 6d25e6a0a5f..46ef0c0a9b9 100644
--- a/src/sage/rings/polynomial/padics/polynomial_padic_flat.py
+++ b/src/sage/rings/polynomial/padics/polynomial_padic_flat.py
@@ -31,7 +31,7 @@ def __init__(self, parent, x=None, check=True, is_gen=False, construct=False, ab
             Polynomial_generic_dense.__init__(self, parent, x, check, is_gen, construct)
             return
         R = parent.base_ring()
-        if sage.rings.fraction_field_element.is_FractionFieldElement(x):
+        if isinstance(x, sage.rings.fraction_field_element.FractionFieldElement):
             if x.denominator() != 1:
                 raise TypeError("denominator must be 1")
             else:
diff --git a/src/sage/rings/polynomial/plural.pyx b/src/sage/rings/polynomial/plural.pyx
index 6a600f74f53..d78464e1deb 100644
--- a/src/sage/rings/polynomial/plural.pyx
+++ b/src/sage/rings/polynomial/plural.pyx
@@ -120,7 +120,7 @@ import sage.libs.singular.ring
 
 from sage.rings.finite_rings.finite_field_prime_modn import FiniteField_prime_modn
 from sage.rings.integer cimport Integer
-from sage.rings.integer_ring import is_IntegerRing
+from sage.rings.integer_ring import IntegerRing_class
 
 from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomialRing_libsingular, MPolynomial_libsingular, new_MP
 from sage.rings.polynomial.multi_polynomial_ideal import NCPolynomialIdeal
@@ -532,7 +532,7 @@ cdef class NCPolynomialRing_plural(Ring):
                     _p = p_NSet(_n, _ring)
 
             # also accepting ZZ
-            elif is_IntegerRing(element.parent()):
+            elif isinstance(element.parent(), IntegerRing_class):
                 if isinstance(base_ring, FiniteField_prime_modn):
                     _p = p_ISet(int(element),_ring)
                 else:
diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index 1270c42ce2a..370f864c2fb 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -54,7 +54,6 @@ AUTHORS:
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-cdef is_FractionField
 cdef ZZ, QQ, RR, CC, RDF, CDF
 
 cimport cython
@@ -103,11 +102,11 @@ from sage.structure.element import coerce_binop
 from sage.structure.element cimport (parent, have_same_parent,
         Element, RingElement)
 
-from sage.rings.rational_field import QQ, is_RationalField
-from sage.rings.integer_ring import ZZ, is_IntegerRing
+from sage.rings.rational_field import QQ, RationalField
+from sage.rings.integer_ring import ZZ, IntegerRing_class
 from sage.rings.integer cimport Integer, smallInteger
 from sage.libs.gmp.mpz cimport *
-from sage.rings.fraction_field import FractionField, is_FractionField
+from sage.rings.fraction_field import FractionField
 from sage.rings.padics.padic_generic import pAdicGeneric
 
 from sage.structure.category_object cimport normalize_names
@@ -5026,7 +5025,7 @@ cdef class Polynomial(CommutativePolynomial):
 
         n = None
 
-        if isinstance(R, sage.rings.abc.IntegerModRing) or is_IntegerRing(R):
+        if isinstance(R, sage.rings.abc.IntegerModRing) or isinstance(R, IntegerRing_class):
             try:
                 G = list(self._pari_with_name().factor())
             except PariError:
@@ -5840,7 +5839,7 @@ cdef class Polynomial(CommutativePolynomial):
         if self.degree() <= 1:
             return R.fraction_field()
 
-        if is_IntegerRing(R):
+        if isinstance(R, IntegerRing_class):
             from sage.rings.number_field.number_field import NumberField
             return NumberField(self, names)
 
@@ -6411,7 +6410,7 @@ cdef class Polynomial(CommutativePolynomial):
         from sage.categories.number_fields import NumberFields
 
         K = self.base_ring()
-        if K in NumberFields() or isinstance(K, sage.rings.abc.Order) or is_IntegerRing(K):
+        if K in NumberFields() or isinstance(K, sage.rings.abc.Order) or isinstance(K, IntegerRing_class):
             from sage.schemes.projective.projective_space import ProjectiveSpace
             P = ProjectiveSpace(K, self.number_of_terms() - 1)
             return P.point(self.coefficients()).global_height(prec=prec)
@@ -8931,7 +8930,7 @@ cdef class Polynomial(CommutativePolynomial):
         if L != K or isinstance(L, sage.rings.abc.AlgebraicField_common):
             # So far, the only "special" implementations are for real
             # and complex root isolation and for p-adic factorization
-            if (is_IntegerRing(K) or is_RationalField(K)
+            if (isinstance(K, IntegerRing_class) or isinstance(K, RationalField)
                 or isinstance(K, sage.rings.abc.AlgebraicRealField)) and \
                 isinstance(L, (sage.rings.abc.AlgebraicRealField, sage.rings.abc.RealIntervalField)):
 
@@ -8961,7 +8960,7 @@ cdef class Polynomial(CommutativePolynomial):
                 else:
                     return [rt for (rt, mult) in rts]
 
-            if (is_IntegerRing(K) or is_RationalField(K)
+            if (isinstance(K, IntegerRing_class) or isinstance(K, RationalField)
                 or isinstance(K, sage.rings.abc.AlgebraicField_common) or input_gaussian) and \
                 isinstance(L, (sage.rings.abc.ComplexIntervalField, sage.rings.abc.AlgebraicField_common)):
 
@@ -9992,8 +9991,8 @@ cdef class Polynomial(CommutativePolynomial):
             else:
                 raise NotImplementedError
         else:
-            from sage.rings.fraction_field import is_FractionField
-            if is_FractionField(p.parent()) and self._parent.has_coerce_map_from(p.parent().ring()):
+            from sage.rings.fraction_field import FractionField_generic
+            if isinstance(p.parent(), FractionField_generic) and self._parent.has_coerce_map_from(p.parent().ring()):
                 _p = self._parent.coerce(p.parent().ring()(p)) # here we require that p be integral.
             else:
                 raise TypeError("The polynomial, p, must have the same parent as self.")
@@ -11983,7 +11982,7 @@ cdef class Polynomial_generic_dense(Polynomial):
                 self._coeffs = x
             return
 
-        if sage.rings.fraction_field_element.is_FractionFieldElement(x):
+        if isinstance(x, sage.rings.fraction_field_element.FractionFieldElement):
             if x.denominator() != 1:
                 raise TypeError("denominator must be 1")
             else:
diff --git a/src/sage/rings/polynomial/polynomial_singular_interface.py b/src/sage/rings/polynomial/polynomial_singular_interface.py
index 3d066e68631..ee7c243087f 100644
--- a/src/sage/rings/polynomial/polynomial_singular_interface.py
+++ b/src/sage/rings/polynomial/polynomial_singular_interface.py
@@ -40,7 +40,7 @@
 import sage.rings.abc
 import sage.rings.number_field as number_field
 
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.rings.function_field.function_field_rational import RationalFunctionField
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.integer_ring import ZZ
@@ -74,7 +74,7 @@ def _do_singular_init_(singular, base_ring, char, _vars, order):
     if base_ring is ZZ:
         return make_ring("(ZZ)"), None
 
-    if sage.rings.rational_field.is_RationalField(base_ring):
+    if isinstance(base_ring, sage.rings.rational_field.RationalField):
         return make_ring("(QQ)"), None
 
     elif isinstance(base_ring, sage.rings.abc.RealField):
@@ -136,7 +136,7 @@ def _do_singular_init_(singular, base_ring, char, _vars, order):
 
         return R, minpoly
 
-    elif sage.rings.fraction_field.is_FractionField(base_ring):
+    elif isinstance(base_ring, sage.rings.fraction_field.FractionField_generic):
         if base_ring.ngens() == 1:
             gens = str(base_ring.gen())
         else:
@@ -430,7 +430,7 @@ def can_convert_to_singular(R):
 
     base_ring = R.base_ring()
     if (base_ring is ZZ
-        or is_RationalField(base_ring)
+        or isinstance(base_ring, RationalField)
         or isinstance(base_ring, (sage.rings.abc.IntegerModRing,
                                   sage.rings.abc.RealField, sage.rings.abc.ComplexField,
                                   sage.rings.abc.RealDoubleField, sage.rings.abc.ComplexDoubleField))):
@@ -439,7 +439,7 @@ def can_convert_to_singular(R):
         return base_ring.characteristic() <= 2147483647
     elif isinstance(base_ring, NumberField):
         return base_ring.is_absolute()
-    elif sage.rings.fraction_field.is_FractionField(base_ring):
+    elif isinstance(base_ring, sage.rings.fraction_field.FractionField_generic):
         B = base_ring.base_ring()
         return (B.is_prime_field() or B is ZZ
                 or (isinstance(B, FiniteField) and B.characteristic() <= 2147483647))
diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index f6d391679a6..17b8559e34c 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -594,7 +594,7 @@
 from sage.rings import infinity
 from sage.rings.cc import CC
 from sage.rings.cif import CIF
-from sage.rings.complex_interval import is_ComplexIntervalFieldElement
+from sage.rings.complex_interval import ComplexIntervalFieldElement
 from sage.rings.complex_interval_field import ComplexIntervalField
 from sage.rings.integer_ring import ZZ
 from sage.rings.number_field.number_field import (
@@ -613,7 +613,7 @@
     RIF,
     RealIntervalField,
     RealIntervalField_class,
-    is_RealIntervalFieldElement,
+    RealIntervalFieldElement,
 )
 from sage.rings.real_mpfr import RR
 from sage.structure.coerce import parent_is_numerical, parent_is_real_numerical
@@ -1436,7 +1436,7 @@ def polynomial_root(self, poly, interval, multiplicity=1):
             sage: r = AA.polynomial_root(p, RIF(1, 2)); r^3
             2.000000000000000?
         """
-        if not is_RealIntervalFieldElement(interval):
+        if not isinstance(interval, RealIntervalFieldElement):
             raise ValueError("interval argument of .polynomial_root on algebraic real field must be real")
 
         return AlgebraicReal(ANRoot(poly, interval, multiplicity))
@@ -2489,7 +2489,7 @@ def conjugate_expand(v):
         sage: conjugate_expand(RIF(1, 2)).str(style='brackets')
         '[1.0000000000000000 .. 2.0000000000000000]'
     """
-    if is_RealIntervalFieldElement(v):
+    if isinstance(v, RealIntervalFieldElement):
         return v
     im = v.imag()
     if not im.contains_zero():
@@ -2522,7 +2522,7 @@ def conjugate_shrink(v):
         sage: conjugate_shrink(CIF(RIF(1, 2), RIF(-1, 2))).str(style='brackets')
         '[1.0000000000000000 .. 2.0000000000000000]'
     """
-    if is_RealIntervalFieldElement(v):
+    if isinstance(v, RealIntervalFieldElement):
         return v
     im = v.imag()
     if im.contains_zero():
@@ -4507,9 +4507,9 @@ def _set_descr(self, new_descr):
         """
         self._descr = new_descr
         new_val = self._descr._interval_fast(self.parent().default_interval_prec())
-        if is_RealIntervalFieldElement(new_val) and is_ComplexIntervalFieldElement(self._value):
+        if isinstance(new_val, RealIntervalFieldElement) and isinstance(self._value, ComplexIntervalFieldElement):
             self._value = self._value.real().intersection(new_val)
-        elif is_RealIntervalFieldElement(self._value) and is_ComplexIntervalFieldElement(new_val):
+        elif isinstance(self._value, RealIntervalFieldElement) and isinstance(new_val, ComplexIntervalFieldElement):
             self._value = self._value.intersection(new_val.real())
         else:
             self._value = self._value.intersection(new_val)
@@ -4757,7 +4757,7 @@ def interval(self, field):
         target = RR(1.0) >> field.prec()
         val = self.interval_diameter(target)
         if (isinstance(field, (RealIntervalField_class, RealBallField))
-                and is_ComplexIntervalFieldElement(val)):
+                and isinstance(val, ComplexIntervalFieldElement)):
             if val.imag().is_zero():
                 return field(val.real())
             elif self.imag().is_zero():
@@ -4826,7 +4826,7 @@ def radical_expression(self):
 
         # Adapted from NumberFieldElement._symbolic_()
         poly = self.minpoly()
-        if is_ComplexIntervalFieldElement(self._value):
+        if isinstance(self._value, ComplexIntervalFieldElement):
             interval_field = self._value.parent()
         else:
             interval_field = ComplexIntervalField(self._value.prec())
@@ -5484,7 +5484,7 @@ def _ensure_real(self):
             sage: type(b._value)
             <class 'sage.rings.real_mpfi.RealIntervalFieldElement'>
         """
-        if is_ComplexIntervalFieldElement(self._value):
+        if isinstance(self._value, ComplexIntervalFieldElement):
             self._value = self._value.real()
 
     def _more_precision(self):
@@ -6467,7 +6467,7 @@ def _act_(self, e, x):
                         argument = argument - 2 * argument.parent().pi()
             else:
                 val = x._interval_fast(prec)
-                if is_RealIntervalFieldElement(val) or not val.crosses_log_branch_cut():
+                if isinstance(val, RealIntervalFieldElement) or not val.crosses_log_branch_cut():
                     argument = val.argument()
                     if val.imag().is_zero() and val.real() < 0:
                         argument_is_pi = True
@@ -6749,12 +6749,20 @@ def is_AlgebraicReal(x):
 
         sage: from sage.rings.qqbar import is_AlgebraicReal
         sage: is_AlgebraicReal(AA(sqrt(2)))                                             # needs sage.symbolic
+        doctest:warning...
+        DeprecationWarning: The function is_AlgebraicReal is deprecated;
+        use 'isinstance(..., AlgebraicReal)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: is_AlgebraicReal(QQbar(sqrt(2)))                                          # needs sage.symbolic
         False
         sage: is_AlgebraicReal("spam")
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38128,
+                "The function is_AlgebraicReal is deprecated; "
+                "use 'isinstance(..., AlgebraicReal)' instead.")
     return isinstance(x, AlgebraicReal)
 
 
@@ -6766,12 +6774,20 @@ def is_AlgebraicNumber(x):
 
         sage: from sage.rings.qqbar import is_AlgebraicNumber
         sage: is_AlgebraicNumber(AA(sqrt(2)))                                           # needs sage.symbolic
+        doctest:warning...
+        DeprecationWarning: The function is_AlgebraicNumber is deprecated;
+        use 'isinstance(..., AlgebraicNumber)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         False
         sage: is_AlgebraicNumber(QQbar(sqrt(2)))                                        # needs sage.symbolic
         True
         sage: is_AlgebraicNumber("spam")
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38128,
+                "The function is_AlgebraicNumber is deprecated; "
+                "use 'isinstance(..., AlgebraicNumber)' instead.")
     return isinstance(x, AlgebraicNumber)
 
 
@@ -7052,7 +7068,7 @@ def __init__(self, poly, interval, multiplicity=1):
             poly = AlgebraicPolynomialTracker(poly)
         self._poly = poly
         self._multiplicity = multiplicity
-        self._complex = is_ComplexIntervalFieldElement(interval)
+        self._complex = isinstance(interval, ComplexIntervalFieldElement)
         self._complex_poly = poly.is_complex()
         self._interval = self.refine_interval(interval, 64)
 
@@ -7138,7 +7154,7 @@ def handle_sage_input(self, sib, coerce, is_qqbar):
         intv = self._interval
         # Check whether a 53-bit interval actually isolates the root.
         # If so, use it, because 53-bit intervals print prettier.
-        if is_ComplexIntervalFieldElement(intv):
+        if isinstance(intv, ComplexIntervalFieldElement):
             loose_intv = CIF(intv)
         else:
             loose_intv = RIF(intv)
@@ -7988,7 +8004,7 @@ def simplify(self, n):
     def _interval_fast(self, prec):
         gen_val = self._generator._interval_fast(prec)
         v = self._value.polynomial()(gen_val)
-        if self._exactly_real and is_ComplexIntervalFieldElement(v):
+        if self._exactly_real and isinstance(v, ComplexIntervalFieldElement):
             return v.real()
         return v
 
@@ -8337,7 +8353,7 @@ def _interval_fast(self, prec):
 
         v = self._arg._interval_fast(prec)
 
-        if not is_ComplexIntervalFieldElement(v):
+        if not isinstance(v, ComplexIntervalFieldElement):
             self._complex = False
 
         if op == '-':
@@ -8347,7 +8363,7 @@ def _interval_fast(self, prec):
             return ~v
 
         if op == 'conjugate':
-            if is_ComplexIntervalFieldElement(v):
+            if isinstance(v, ComplexIntervalFieldElement):
                 return v.conjugate()
             else:
                 return v
@@ -8355,13 +8371,13 @@ def _interval_fast(self, prec):
         self._complex = False
 
         if op == 'real':
-            if is_ComplexIntervalFieldElement(v):
+            if isinstance(v, ComplexIntervalFieldElement):
                 return v.real()
             else:
                 return v
 
         if op == 'imag':
-            if is_ComplexIntervalFieldElement(v):
+            if isinstance(v, ComplexIntervalFieldElement):
                 return v.imag()
             else:
                 return RealIntervalField(prec)(0)
@@ -8370,7 +8386,7 @@ def _interval_fast(self, prec):
             return abs(v)
 
         if op == 'norm':
-            if is_ComplexIntervalFieldElement(v):
+            if isinstance(v, ComplexIntervalFieldElement):
                 return v.norm()
             else:
                 return v.square()
@@ -8611,7 +8627,7 @@ def _interval_fast(self, prec):
         lv = self._left._interval_fast(prec)
         rv = self._right._interval_fast(prec)
 
-        if not (is_ComplexIntervalFieldElement(lv) or is_ComplexIntervalFieldElement(rv)):
+        if not (isinstance(lv, ComplexIntervalFieldElement) or isinstance(rv, ComplexIntervalFieldElement)):
             self._complex = False
 
         return op(lv, rv)
diff --git a/src/sage/rings/rational.pyx b/src/sage/rings/rational.pyx
index 1faece8f298..819a85dbc35 100644
--- a/src/sage/rings/rational.pyx
+++ b/src/sage/rings/rational.pyx
@@ -393,6 +393,10 @@ def is_Rational(x):
 
         sage: from sage.rings.rational import is_Rational
         sage: is_Rational(2)
+        doctest:warning...
+        DeprecationWarning: The function is_Rational is deprecated;
+        use 'isinstance(..., Rational)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         False
         sage: is_Rational(2/1)
         True
@@ -401,6 +405,10 @@ def is_Rational(x):
         sage: is_Rational('5')
         False
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_Rational is deprecated; "
+                       "use 'isinstance(..., Rational)' instead.")
     return isinstance(x, Rational)
 
 
diff --git a/src/sage/rings/rational_field.py b/src/sage/rings/rational_field.py
index 5234ea105e2..62d85cf3380 100644
--- a/src/sage/rings/rational_field.py
+++ b/src/sage/rings/rational_field.py
@@ -1701,10 +1701,18 @@ def is_RationalField(x) -> bool:
 
         sage: from sage.rings.rational_field import is_RationalField as is_RF
         sage: is_RF(QQ)
+        doctest:warning...
+        DeprecationWarning: The function is_RationalField is deprecated;
+        use 'isinstance(..., RationalField)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: is_RF(ZZ)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38128,
+                "The function is_RationalField is deprecated; "
+                "use 'isinstance(..., RationalField)' instead.")
     return isinstance(x, RationalField)
 
 
diff --git a/src/sage/rings/real_double.pyx b/src/sage/rings/real_double.pyx
index de1f843ce87..d0ef9a4bb62 100644
--- a/src/sage/rings/real_double.pyx
+++ b/src/sage/rings/real_double.pyx
@@ -2055,10 +2055,18 @@ def is_RealDoubleElement(x):
 
         sage: from sage.rings.real_double import is_RealDoubleElement
         sage: is_RealDoubleElement(RDF(3))
+        doctest:warning...
+        DeprecationWarning: The function is_RealDoubleElement is deprecated;
+        use 'isinstance(..., RealDoubleElement)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: is_RealDoubleElement(RIF(3))                                              # needs sage.rings.real_interval_field
         False
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_RealDoubleElement is deprecated; "
+                       "use 'isinstance(..., RealDoubleElement)' instead.")
     return isinstance(x, RealDoubleElement)
 
 
diff --git a/src/sage/rings/real_mpfi.pyx b/src/sage/rings/real_mpfi.pyx
index 7007f1da8d7..95b472e912c 100644
--- a/src/sage/rings/real_mpfi.pyx
+++ b/src/sage/rings/real_mpfi.pyx
@@ -5332,10 +5332,18 @@ def is_RealIntervalField(x):
     EXAMPLES::
 
         sage: sage.rings.real_mpfi.is_RealIntervalField(RIF)
+        doctest:warning...
+        DeprecationWarning: The function is_RealIntervalField is deprecated;
+        use 'isinstance(..., RealIntervalField_class)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: sage.rings.real_mpfi.is_RealIntervalField(RealIntervalField(200))
         True
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_RealIntervalField is deprecated; "
+                       "use 'isinstance(..., RealIntervalField_class)' instead.")
     return isinstance(x, RealIntervalField_class)
 
 
@@ -5346,10 +5354,18 @@ def is_RealIntervalFieldElement(x):
     EXAMPLES::
 
         sage: sage.rings.real_mpfi.is_RealIntervalFieldElement(RIF(2.2))
+        doctest:warning...
+        DeprecationWarning: The function is_RealIntervalFieldElement is deprecated;
+        use 'isinstance(..., RealIntervalFieldElement)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: sage.rings.real_mpfi.is_RealIntervalFieldElement(RealIntervalField(200)(2.2))
         True
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_RealIntervalFieldElement is deprecated; "
+                       "use 'isinstance(..., RealIntervalFieldElement)' instead.")
     return isinstance(x, RealIntervalFieldElement)
 
 
diff --git a/src/sage/rings/real_mpfr.pyx b/src/sage/rings/real_mpfr.pyx
index 885003ed7f8..9e905c9c721 100644
--- a/src/sage/rings/real_mpfr.pyx
+++ b/src/sage/rings/real_mpfr.pyx
@@ -5886,6 +5886,10 @@ def is_RealNumber(x):
 
         sage: from sage.rings.real_mpfr import is_RealNumber
         sage: is_RealNumber(2.5)
+        doctest:warning...
+        DeprecationWarning: The function is_RealNumber is deprecated;
+        use 'isinstance(..., RealNumber)' instead.
+        See https://github.com/sagemath/sage/issues/38128 for details.
         True
         sage: is_RealNumber(float(2.3))
         False
@@ -5894,6 +5898,10 @@ def is_RealNumber(x):
         sage: is_RealNumber(pi)                                                         # needs sage.symbolic
         False
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38128,
+                       "The function is_RealNumber is deprecated; "
+                       "use 'isinstance(..., RealNumber)' instead.")
     return isinstance(x, RealNumber)
 
 
diff --git a/src/sage/schemes/affine/affine_homset.py b/src/sage/schemes/affine/affine_homset.py
index 1a5dd8477ab..f90bcfffec1 100644
--- a/src/sage/schemes/affine/affine_homset.py
+++ b/src/sage/schemes/affine/affine_homset.py
@@ -38,7 +38,7 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.real_mpfr import RR
 from sage.rings.cc import CC
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.categories.fields import Fields
 from sage.categories.number_fields import NumberFields
 from sage.rings.finite_rings.finite_field_base import FiniteField
@@ -349,7 +349,7 @@ def points(self, **kwds):
         B = kwds.pop('bound', 0)
         tol = kwds.pop('tolerance', 1e-2)
         prec = kwds.pop('precision', 53)
-        if is_RationalField(R) or R == ZZ:
+        if isinstance(R, RationalField) or R == ZZ:
             if not B > 0:
                 raise TypeError("a positive bound B (= %s) must be specified" % B)
             from sage.schemes.affine.affine_rational_point import enum_affine_rational_field
diff --git a/src/sage/schemes/affine/affine_space.py b/src/sage/schemes/affine/affine_space.py
index 572d39bad51..889d9005ed6 100644
--- a/src/sage/schemes/affine/affine_space.py
+++ b/src/sage/schemes/affine/affine_space.py
@@ -14,7 +14,7 @@
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.rational_field import is_RationalField
+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.finite_rings.finite_field_base import FiniteField
@@ -1063,7 +1063,7 @@ def points_of_bounded_height(self, **kwds):
             sage: len(list(A.points_of_bounded_height(bound=2, tolerance=0.1)))         # needs sage.rings.number_field
             529
         """
-        if is_RationalField(self.base_ring()):
+        if isinstance(self.base_ring(), RationalField):
             ftype = False  # stores whether field is a number field or the rational field
         elif self.base_ring() in NumberFields():  # true for rational field as well, so check is_RationalField first
             ftype = True
diff --git a/src/sage/schemes/berkovich/berkovich_cp_element.py b/src/sage/schemes/berkovich/berkovich_cp_element.py
index bd641bd05a2..a9299e4e732 100644
--- a/src/sage/schemes/berkovich/berkovich_cp_element.py
+++ b/src/sage/schemes/berkovich/berkovich_cp_element.py
@@ -36,7 +36,7 @@
 from sage.structure.element import Element
 from sage.structure.element import Expression
 import sage.rings.abc
-from sage.rings.real_mpfr import RR, is_RealNumber
+from sage.rings.real_mpfr import RR, RealNumber
 from sage.rings.padics.padic_generic_element import pAdicGenericElement
 from sage.rings.padics.padic_base_generic import pAdicBaseGeneric
 from sage.schemes.projective.projective_space import ProjectiveSpace
@@ -215,7 +215,7 @@ def __init__(self, parent, center, radius=None, power=None, prec=20, space_type=
                     # since we are over a field, we can normalize coordinates. all code assumes normalized coordinates
                     center.normalize_coordinates()
                     # make sure the radius coerces into the reals
-                    if not is_RealNumber(radius):
+                    if not isinstance(radius, RealNumber):
                         if isinstance(radius, Expression):
                             radius = RR(radius)
                         elif RR.has_coerce_map_from(radius.parent()):
@@ -258,7 +258,7 @@ def __init__(self, parent, center, radius=None, power=None, prec=20, space_type=
                             except (TypeError, ValueError):
                                 raise ValueError('could not convert %s to %s' % (center, self._base_space))
                     # make sure the radius coerces into the reals
-                    if not is_RealNumber(radius):
+                    if not isinstance(radius, RealNumber):
                         if isinstance(radius, Expression):
                             radius = RR(radius)
                         elif RR.has_coerce_map_from(radius.parent()):
@@ -388,7 +388,7 @@ def __init__(self, parent, center, radius=None, power=None, prec=20, space_type=
                         raise ValueError('radius univariate function but center is constant. ' +
                                          'this does not define a type IV point')
                     raise TypeError("symbolic radius must be a real number")
-            if (not is_RealNumber(radius)) and power is None:
+            if (not isinstance(radius, RealNumber)) and power is None:
                 if RR.has_coerce_map_from(radius.parent()):
                     self._radius = RR(radius)
                 else:
diff --git a/src/sage/schemes/curves/affine_curve.py b/src/sage/schemes/curves/affine_curve.py
index f8e5dc4bfbe..dbdb2dfa4cd 100644
--- a/src/sage/schemes/curves/affine_curve.py
+++ b/src/sage/schemes/curves/affine_curve.py
@@ -145,7 +145,7 @@
 from sage.rings.polynomial.multi_polynomial_element import degree_lowest_rational_function
 from sage.rings.number_field.number_field import NumberField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.rings.infinity import infinity
 
 from sage.schemes.affine.affine_space import AffineSpace, AffineSpace_generic
@@ -1548,10 +1548,10 @@ def extension(self):
             pts = self.change_ring(F.embeddings(QQbar)[0]).rational_points()
             L = [t for pt in pts for t in pt]
             K = number_field_elements_from_algebraics(L)[0]
-            if is_RationalField(K):
+            if isinstance(K, RationalField):
                 return F.embeddings(F)[0]
             else:
-                if is_RationalField(F):
+                if isinstance(F, RationalField):
                     return F.embeddings(K)[0]
                 else:
                     # make sure the defining polynomial variable names are the same for K, N
diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
index cec2e08e96b..6045cc3ea70 100644
--- a/src/sage/schemes/curves/projective_curve.py
+++ b/src/sage/schemes/curves/projective_curve.py
@@ -154,7 +154,7 @@
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.qqbar import (number_field_elements_from_algebraics,
                               QQbar)
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.rings.integer import Integer
 
 from sage.schemes.projective.projective_space import ProjectiveSpace, ProjectiveSpace_ring
@@ -1458,10 +1458,10 @@ def extension(self):
             pts = self.change_ring(F.embeddings(QQbar)[0]).rational_points()
             L = [t for pt in pts for t in pt]
             K = number_field_elements_from_algebraics(L)[0]
-            if is_RationalField(K):
+            if isinstance(K, RationalField):
                 return F.embeddings(F)[0]
             else:
-                if is_RationalField(F):
+                if isinstance(F, RationalField):
                     return F.embeddings(K)[0]
                 else:
                     # make sure the defining polynomial variable names are the same for K, N
@@ -1862,7 +1862,7 @@ def rational_parameterization(self):
         """
         if self.genus():
             raise TypeError("this curve must have geometric genus zero")
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise TypeError("this curve must be defined over the rational field")
         singular.lib("paraplanecurves.lib")
         R = singular.paraPlaneCurve(self.defining_polynomial())
diff --git a/src/sage/schemes/generic/algebraic_scheme.py b/src/sage/schemes/generic/algebraic_scheme.py
index f442ff309b3..8cc0e544917 100644
--- a/src/sage/schemes/generic/algebraic_scheme.py
+++ b/src/sage/schemes/generic/algebraic_scheme.py
@@ -118,7 +118,7 @@
 
 from sage.rings.ideal import is_Ideal
 from sage.rings.integer_ring import ZZ
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.rings.finite_rings.finite_field_base import FiniteField
 
 from sage.misc.latex import latex
@@ -873,7 +873,7 @@ def rational_points(self, **kwds):
             F = self.base_ring()
 
         if bound == 0:
-            if is_RationalField(F):
+            if isinstance(F, RationalField):
                 raise TypeError("A positive bound (= %s) must be specified." % bound)
             if not isinstance(F, FiniteField):
                 raise TypeError("Argument F (= %s) must be a finite field." % F)
diff --git a/src/sage/schemes/generic/morphism.py b/src/sage/schemes/generic/morphism.py
index 9986dea97ff..8034d0b9b5a 100644
--- a/src/sage/schemes/generic/morphism.py
+++ b/src/sage/schemes/generic/morphism.py
@@ -82,7 +82,7 @@
 from sage.structure.sequence import Sequence
 from sage.categories.homset import Homset, Hom, End
 from sage.rings.fraction_field_element import FractionFieldElement
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.categories.map import FormalCompositeMap, Map
 from sage.misc.constant_function import ConstantFunction
 from sage.misc.lazy_attribute import lazy_attribute
@@ -1643,7 +1643,7 @@ def specialization(self, D=None, phi=None, homset=None):
             if phi is None:
                 raise ValueError("either the dictionary or the specialization must be provided")
         else:
-            if is_FractionField(self[0].parent()):
+            if isinstance(self[0].parent(), FractionField_generic):
                 from sage.rings.polynomial.flatten import FractionSpecializationMorphism
                 phi = FractionSpecializationMorphism(self[0].parent(), D)
             else:
diff --git a/src/sage/schemes/hyperelliptic_curves/constructor.py b/src/sage/schemes/hyperelliptic_curves/constructor.py
index 16526fec853..46d01cfd2cb 100644
--- a/src/sage/schemes/hyperelliptic_curves/constructor.py
+++ b/src/sage/schemes/hyperelliptic_curves/constructor.py
@@ -26,7 +26,7 @@
 
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.polynomial_element import Polynomial
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.structure.dynamic_class import dynamic_class
 
 
@@ -269,20 +269,14 @@ def HyperellipticCurve(f, h=0, names=None, PP=None, check_squarefree=True):
 
     # For certain base fields, we specialise to subclasses
     # with special case methods
-    def is_FiniteField(x):
-        return isinstance(x, FiniteField)
-
-    def is_pAdicField(x):
-        return isinstance(x, sage.rings.abc.pAdicField)
-
     fields = [
-        ("FiniteField", is_FiniteField, HyperellipticCurve_finite_field),
-        ("RationalField", is_RationalField, HyperellipticCurve_rational_field),
-        ("pAdicField", is_pAdicField, HyperellipticCurve_padic_field),
+        ("FiniteField", FiniteField, HyperellipticCurve_finite_field),
+        ("RationalField", RationalField, HyperellipticCurve_rational_field),
+        ("pAdicField", sage.rings.abc.pAdicField, HyperellipticCurve_padic_field),
     ]
 
-    for name, test, cls in fields:
-        if test(R):
+    for name, base_ring_cls, cls in fields:
+        if isinstance(R, base_ring_cls):
             bases.append(cls)
             cls_name.append(name)
             break
diff --git a/src/sage/schemes/hyperelliptic_curves/jacobian_homset.py b/src/sage/schemes/hyperelliptic_curves/jacobian_homset.py
index 88b28a4b753..2a192248180 100644
--- a/src/sage/schemes/hyperelliptic_curves/jacobian_homset.py
+++ b/src/sage/schemes/hyperelliptic_curves/jacobian_homset.py
@@ -44,7 +44,7 @@
 
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.integer_ring import ZZ
-from sage.rings.integer import is_Integer, Integer
+from sage.rings.integer import Integer
 from sage.rings.polynomial.polynomial_element import Polynomial
 
 from sage.schemes.generic.homset import SchemeHomset_points
@@ -124,16 +124,16 @@ def __call__(self, P):
             elif len(P) == 2:
                 P1 = P[0]
                 P2 = P[1]
-                if is_Integer(P1) and is_Integer(P2):
+                if isinstance(P1, Integer) and isinstance(P2, Integer):
                     R = PolynomialRing(self.value_ring(), 'x')
                     P1 = R(P1)
                     P2 = R(P2)
                     return JacobianMorphism_divisor_class_field(self, (P1, P2))
-                if is_Integer(P1) and isinstance(P2, Polynomial):
+                if isinstance(P1, Integer) and isinstance(P2, Polynomial):
                     R = PolynomialRing(self.value_ring(), 'x')
                     P1 = R(P1)
                     return JacobianMorphism_divisor_class_field(self, (P1, P2))
-                if is_Integer(P2) and isinstance(P1, Polynomial):
+                if isinstance(P2, Integer) and isinstance(P1, Polynomial):
                     R = PolynomialRing(self.value_ring(), 'x')
                     P2 = R(P2)
                     return JacobianMorphism_divisor_class_field(self, (P1, P2))
diff --git a/src/sage/schemes/plane_conics/con_number_field.py b/src/sage/schemes/plane_conics/con_number_field.py
index f044b884932..393b77bc1ff 100644
--- a/src/sage/schemes/plane_conics/con_number_field.py
+++ b/src/sage/schemes/plane_conics/con_number_field.py
@@ -21,7 +21,7 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from .con_field import ProjectiveConic_field
 
@@ -305,7 +305,7 @@ def has_rational_point(self, point=False, obstruction=False,
                 if point or obstruction:
                     return True, pt
                 return True
-            if is_RationalField(B):
+            if isinstance(B, RationalField):
                 K = B
                 [KtoB, BtoK] = [K.hom(K) for i in range(2)]
             else:
diff --git a/src/sage/schemes/plane_conics/con_rational_function_field.py b/src/sage/schemes/plane_conics/con_rational_function_field.py
index fec1a50fdbb..bc842415d8e 100644
--- a/src/sage/schemes/plane_conics/con_rational_function_field.py
+++ b/src/sage/schemes/plane_conics/con_rational_function_field.py
@@ -44,7 +44,7 @@
 from sage.arith.functions import lcm
 from sage.arith.misc import GCD as gcd
 from sage.modules.free_module_element import vector
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 
 
 class ProjectiveConic_rational_function_field(ProjectiveConic_field):
@@ -392,7 +392,7 @@ def _reduce_conic(self):
 
         # remove squares
         for i, x in enumerate(coeff):
-            if is_FractionField(x.parent()):
+            if isinstance(x.parent(), FractionField_generic):
                 # go to base ring of fraction field
                 x = self.base().base()(x)
 
diff --git a/src/sage/schemes/plane_conics/constructor.py b/src/sage/schemes/plane_conics/constructor.py
index 10e158514dc..308b56f6db0 100644
--- a/src/sage/schemes/plane_conics/constructor.py
+++ b/src/sage/schemes/plane_conics/constructor.py
@@ -26,9 +26,9 @@
 from sage.matrix.constructor import matrix
 from sage.modules.free_module_element import vector
 from sage.categories.integral_domains import IntegralDomains
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.rings.finite_rings.finite_field_base import FiniteField
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 
 from sage.rings.number_field.number_field_base import NumberField
 from sage.rings.polynomial.multi_polynomial import MPolynomial
@@ -238,11 +238,11 @@ def Conic(base_field, F=None, names=None, unique=True):
         P2 = ProjectiveSpace(2, base_field, names)
         if isinstance(base_field, FiniteField):
             return ProjectiveConic_finite_field(P2, F)
-        if is_RationalField(base_field):
+        if isinstance(base_field, RationalField):
             return ProjectiveConic_rational_field(P2, F)
         if isinstance(base_field, NumberField):
             return ProjectiveConic_number_field(P2, F)
-        if is_FractionField(base_field) and (is_PolynomialRing(base_field.ring()) or is_MPolynomialRing(base_field.ring())):
+        if isinstance(base_field, FractionField_generic) and (is_PolynomialRing(base_field.ring()) or is_MPolynomialRing(base_field.ring())):
             return ProjectiveConic_rational_function_field(P2, F)
 
         return ProjectiveConic_field(P2, F)
diff --git a/src/sage/schemes/product_projective/homset.py b/src/sage/schemes/product_projective/homset.py
index 590030762e1..ef135a2cd6b 100644
--- a/src/sage/schemes/product_projective/homset.py
+++ b/src/sage/schemes/product_projective/homset.py
@@ -23,7 +23,7 @@
 from sage.misc.mrange import xmrange
 from sage.misc.misc_c import prod
 from sage.rings.finite_rings.finite_field_base import FiniteField
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.schemes.generic.algebraic_scheme import AlgebraicScheme_subscheme
 from sage.schemes.generic.homset import SchemeHomset_points
 
@@ -199,7 +199,7 @@ def points(self, **kwds):
                 return list(points)
         R = self.value_ring()
         points = []
-        if is_RationalField(R):
+        if isinstance(R, RationalField):
             if not B > 0:
                 raise TypeError("a positive bound B (= %s) must be specified" % B)
             alg = kwds.pop('algorithm', None)
diff --git a/src/sage/schemes/projective/projective_homset.py b/src/sage/schemes/projective/projective_homset.py
index a64ceabca4e..bc1a781c00b 100644
--- a/src/sage/schemes/projective/projective_homset.py
+++ b/src/sage/schemes/projective/projective_homset.py
@@ -44,7 +44,7 @@
 
 from sage.misc.verbose import verbose
 
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 from sage.categories.fields import Fields
 from sage.categories.number_fields import NumberFields
 from sage.rings.finite_rings.finite_field_base import FiniteField
@@ -274,7 +274,7 @@ def points(self, **kwds):
         B = kwds.pop('bound', 0)
         tol = kwds.pop('tolerance', 1e-2)
         prec = kwds.pop('precision', 53)
-        if is_RationalField(R):
+        if isinstance(R, RationalField):
             if not B > 0:
                 raise TypeError("a positive bound B (= %s) must be specified" % B)
             if isinstance(X, AlgebraicScheme_subscheme): # sieve should only be called for subschemes
diff --git a/src/sage/schemes/projective/projective_space.py b/src/sage/schemes/projective/projective_space.py
index ded40bb85b5..c05588f4698 100644
--- a/src/sage/schemes/projective/projective_space.py
+++ b/src/sage/schemes/projective/projective_space.py
@@ -88,7 +88,7 @@
 from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
 from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.rational_field import QQ, is_RationalField
+from sage.rings.rational_field import QQ, RationalField
 from sage.rings.fraction_field import FractionField
 from sage.rings.number_field.order import Order
 
@@ -264,7 +264,7 @@ def ProjectiveSpace(n, R=None, names=None):
     if R in _Fields:
         if isinstance(R, FiniteField):
             return ProjectiveSpace_finite_field(n, R, names)
-        if is_RationalField(R):
+        if isinstance(R, RationalField):
             return ProjectiveSpace_rational_field(n, R, names)
         else:
             return ProjectiveSpace_field(n, R, names)
@@ -1170,10 +1170,10 @@ def points_of_bounded_height(self, **kwds):
         # or the ring of integers
         is_ring_of_ints = False
 
-        if is_RationalField(R):
+        if isinstance(R, RationalField):
             field_type = False
         elif R in NumberFields():
-            # True for the rational field as well, so check is_RationalField first
+            # True for the rational field as well, so check RationalField first
             field_type = True
         elif (R is ZZ) or (isinstance(R, Order) and R.is_integrally_closed()): # Ensure ring of integers / maximal order
             is_ring_of_ints = True
diff --git a/src/sage/schemes/projective/projective_subscheme.py b/src/sage/schemes/projective/projective_subscheme.py
index f3e93cd65a5..6135a62b1cb 100644
--- a/src/sage/schemes/projective/projective_subscheme.py
+++ b/src/sage/schemes/projective/projective_subscheme.py
@@ -30,7 +30,7 @@
 
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.rational_field import is_RationalField
+from sage.rings.rational_field import RationalField
 
 from sage.schemes.generic.algebraic_scheme import AlgebraicScheme_subscheme
 from sage.schemes.projective.projective_morphism import SchemeMorphism_polynomial_projective_subscheme_field
@@ -975,7 +975,7 @@ def dual(self):
         from sage.libs.singular.function_factory import ff
 
         K = self.base_ring()
-        if not (is_RationalField(K) or K in Fields().Finite()):
+        if not (isinstance(K, RationalField) or K in Fields().Finite()):
             raise NotImplementedError("base ring must be QQ or a finite field")
         I = self.defining_ideal()
         m = I.ngens()
diff --git a/src/sage/schemes/toric/fano_variety.py b/src/sage/schemes/toric/fano_variety.py
index d7772aa2ca4..c17cf7c37d7 100644
--- a/src/sage/schemes/toric/fano_variety.py
+++ b/src/sage/schemes/toric/fano_variety.py
@@ -130,7 +130,7 @@
 
 from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
 from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 
 from sage.schemes.toric.toric_subscheme import AlgebraicScheme_subscheme_toric
 from sage.schemes.toric.variety import (
@@ -1590,7 +1590,7 @@ def add_variables(field, variables):
     """
     if not variables:
         return field
-    if is_FractionField(field):
+    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):
diff --git a/src/sage/sets/set.py b/src/sage/sets/set.py
index 00c604a07d8..2a5c8c86f23 100644
--- a/src/sage/sets/set.py
+++ b/src/sage/sets/set.py
@@ -491,8 +491,8 @@ def __init__(self, X, category=None):
             '<class 'sage.sets.set.Set_object_enumerated_with_category'>'
             and 'Integer Ring'
         """
-        from sage.rings.integer import is_Integer
-        if isinstance(X, int) or is_Integer(X):
+        from sage.rings.integer import Integer
+        if isinstance(X, int) or isinstance(X, Integer):
             # The coercion model will try to call Set_object(0)
             raise ValueError('underlying object cannot be an integer')
 
diff --git a/src/sage/symbolic/ring.pyx b/src/sage/symbolic/ring.pyx
index e7a28be127a..501b0920898 100644
--- a/src/sage/symbolic/ring.pyx
+++ b/src/sage/symbolic/ring.pyx
@@ -207,7 +207,7 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing):
 
             return False
         else:
-            from sage.rings.fraction_field import is_FractionField
+            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.laurent_polynomial_ring_base import LaurentPolynomialRing_generic
@@ -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 is_FractionField(R) or isinstance(R, LaurentPolynomialRing_generic):
+            elif is_PolynomialRing(R) or is_MPolynomialRing(R) 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