diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
index 3b92c79eee7..b4efa9c5f39 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
@@ -5893,8 +5893,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
             base_ring = base_ring.base_ring()
         elif base_ring in FunctionFields():
             base_ring = base_ring.constant_base_field()
-        from sage.rings.number_field.order import is_NumberFieldOrder
-        if not (base_ring in NumberFields() or is_NumberFieldOrder(base_ring)
+        if not (base_ring in NumberFields() or base_ring == ZZ or isinstance(base_ring, sage.rings.abc.Order)
                 or (base_ring in FiniteFields())):
             raise NotImplementedError("incompatible base field, see documentation")
 
diff --git a/src/sage/rings/finite_rings/residue_field.pyx b/src/sage/rings/finite_rings/residue_field.pyx
index 83d78abb2aa..e4e617a33eb 100644
--- a/src/sage/rings/finite_rings/residue_field.pyx
+++ b/src/sage/rings/finite_rings/residue_field.pyx
@@ -184,7 +184,7 @@ from sage.rings.finite_rings.finite_field_constructor import zech_log_bound, Fin
 from sage.rings.finite_rings.finite_field_prime_modn import FiniteField_prime_modn
 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 is_NumberFieldIdeal
+from sage.rings.number_field.number_field_ideal import NumberFieldIdeal
 
 from sage.rings.fraction_field import is_FractionField
 
@@ -345,7 +345,7 @@ class ResidueFieldFactory(UniqueFactory):
                 if not p.ring().base_ring().is_prime_field():
                     # neither of these will work over non-prime fields quite yet.  We should use relative finite field extensions.
                     raise NotImplementedError
-            elif not (is_NumberFieldIdeal(p) or p.ring() is ZZ):
+            elif not (isinstance(p, NumberFieldIdeal) or p.ring() is ZZ):
                 raise NotImplementedError
         if isinstance(names, tuple):
             if names:
@@ -411,7 +411,7 @@ class ResidueFieldFactory(UniqueFactory):
                 raise ValueError("unrecognized finite field type")
 
         # Should generalize to allowing residue fields of relative extensions to be extensions of finite fields.
-        if is_NumberFieldIdeal(p):
+        if isinstance(p, NumberFieldIdeal):
             characteristic = p.smallest_integer()
         else: # ideal of a function field
             characteristic = pring.base_ring().characteristic()
diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index e13806ad619..6fdc550ffe9 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -81,7 +81,7 @@
 
 
 import sage.libs.ntl.all as ntl
-
+import sage.rings.abc
 import sage.rings.complex_mpfr
 from sage.rings.polynomial.polynomial_element import Polynomial
 import sage.rings.real_mpfr
@@ -212,7 +212,7 @@ def proof_flag(t):
 from sage.structure.factory import UniqueFactory
 from . import number_field_element
 from . import number_field_element_quadratic
-from .number_field_ideal import is_NumberFieldIdeal, NumberFieldFractionalIdeal
+from .number_field_ideal import NumberFieldIdeal, NumberFieldFractionalIdeal
 from sage.libs.pari.all import pari, pari_gen
 
 from sage.rings.rational_field import QQ
@@ -1018,6 +1018,9 @@ def is_AbsoluteNumberField(x):
         sage: from sage.rings.number_field.number_field import is_AbsoluteNumberField
         sage: x = polygen(ZZ, 'x')
         sage: is_AbsoluteNumberField(NumberField(x^2 + 1, 'a'))
+        doctest:warning...
+        DeprecationWarning: The function is_AbsoluteNumberField is deprecated; use 'isinstance(..., NumberField_absolute)' instead.
+        See https://github.com/sagemath/sage/issues/38124 for details.
         True
         sage: is_AbsoluteNumberField(NumberField([x^3 + 17, x^2 + 1], 'a'))
         False
@@ -1030,6 +1033,10 @@ def is_AbsoluteNumberField(x):
         sage: is_AbsoluteNumberField(QQ)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38124,
+                "The function is_AbsoluteNumberField is deprecated; "
+                "use 'isinstance(..., NumberField_absolute)' instead.")
     return isinstance(x, NumberField_absolute)
 
 
@@ -6953,8 +6960,7 @@ def residue_field(self, prime, names=None, check=True):
             ...
             ValueError: Fractional ideal (5) is not a prime ideal
         """
-        from sage.rings.number_field.number_field_ideal import is_NumberFieldIdeal
-        if is_NumberFieldIdeal(prime) and prime.number_field() is not self:
+        if isinstance(prime, NumberFieldIdeal) and prime.number_field() is not self:
             raise ValueError("%s is not an ideal of %s" % (prime, self))
         # This allows principal ideals to be specified using a generator:
         try:
@@ -6962,7 +6968,7 @@ def residue_field(self, prime, names=None, check=True):
         except TypeError:
             pass
 
-        if not is_NumberFieldIdeal(prime) or prime.number_field() is not self:
+        if not isinstance(prime, NumberFieldIdeal) or prime.number_field() is not self:
             raise ValueError("%s is not an ideal of %s" % (prime, self))
         if check and not prime.is_prime():
             raise ValueError("%s is not a prime ideal" % prime)
@@ -7088,7 +7094,7 @@ def uniformizer(self, P, others="positive"):
             sage: x in (t^2 + 3*t +1, t^2 - 4*t +1)
             True
         """
-        if not is_NumberFieldIdeal(P):
+        if not isinstance(P, NumberFieldIdeal):
             P = self.ideal(P)
         P = P.pari_prime()
         if others == "positive":
@@ -8444,10 +8450,9 @@ def _coerce_map_from_(self, R):
         """
         if R is int:
             return self._generic_coerce_map(R)
-        elif R in (ZZ, QQ, self.base()):
+        if R in (ZZ, QQ, self.base()):
             return self._generic_coerce_map(R)
-        from sage.rings.number_field.order import is_NumberFieldOrder
-        if is_NumberFieldOrder(R) and self.has_coerce_map_from(R.number_field()):
+        if isinstance(R, sage.rings.abc.Order) and self.has_coerce_map_from(R.number_field()):
             return self._generic_coerce_map(R)
         # R is not QQ by the above tests
         if isinstance(R, number_field_base.NumberField) and R.coerce_embedding() is not None:
@@ -10348,7 +10353,7 @@ def hilbert_symbol(self, a, b, P=None):
                 if P(a) > 0 or P(b) > 0:
                     return 1
                 return -1
-        if not is_NumberFieldIdeal(P):
+        if not isinstance(P, NumberFieldIdeal):
             P = self.ideal(P)
         if P.number_field() is not self:
             raise ValueError("P (=%s) should be an ideal of self (=%s) in hilbert_symbol, not of %s" % (P, self, P.number_field()))
diff --git a/src/sage/rings/number_field/number_field_element.pyx b/src/sage/rings/number_field/number_field_element.pyx
index 844a4ec3162..1b682403909 100644
--- a/src/sage/rings/number_field/number_field_element.pyx
+++ b/src/sage/rings/number_field/number_field_element.pyx
@@ -50,6 +50,7 @@ from sage.libs.gmp.pylong cimport mpz_pythonhash
 from cpython.object cimport Py_EQ, Py_NE, Py_LT, Py_GT, Py_LE, Py_GE
 from sage.structure.richcmp cimport rich_to_bool
 
+import sage.rings.abc
 import sage.rings.polynomial.polynomial_element
 from sage.rings.polynomial.evaluation_ntl cimport ZZX_evaluation_mpfi
 import sage.rings.rational_field
@@ -1663,8 +1664,8 @@ cdef class NumberFieldElement(NumberFieldElement_base):
         if not isinstance(L, NumberField):
             raise ValueError("L (=%s) must be a NumberField in is_norm" % L)
 
-        from sage.rings.number_field.number_field import is_AbsoluteNumberField
-        if is_AbsoluteNumberField(L):
+        from sage.rings.number_field.number_field import NumberField_absolute
+        if isinstance(L, NumberField_absolute):
             Lrel = L.relativize(K.hom(L), L.variable_name() + '0')
             b, x = self.is_norm(Lrel, element=True, proof=proof)
             h = Lrel.structure()[0]
@@ -1803,8 +1804,8 @@ cdef class NumberFieldElement(NumberFieldElement_base):
         - Francis Clarke (2010-12-26)
         """
         K = self.parent()
-        from sage.rings.number_field.number_field_rel import is_RelativeNumberField
-        if (not is_RelativeNumberField(L)) or L.base_field() != K:
+        from sage.rings.number_field.number_field_rel import NumberField_relative
+        if not isinstance(L, NumberField_relative) or L.base_field() != K:
             raise ValueError("L (=%s) must be a relative number field with base field K (=%s) in rnfisnorm" % (L, K))
 
         rnf_data = K.pari_rnfnorm_data(L, proof=proof)
@@ -1988,8 +1989,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             raise ArithmeticError("factorization of 0 is not defined")
 
         K = self.parent()
-        from sage.rings.number_field.order import is_NumberFieldOrder
-        if is_NumberFieldOrder(K):
+        if isinstance(K, sage.rings.abc.Order):
             K = K.number_field()
         fac = K.ideal(self).factor()
         # Check whether all prime ideals in `fac` are principal
@@ -2088,8 +2088,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
         if R.is_field():
             return R.one()
 
-        from sage.rings.number_field.order import is_NumberFieldOrder
-        if not is_NumberFieldOrder(R):
+        if not isinstance(R, sage.rings.abc.Order):
             raise NotImplementedError("gcd() for %r is not implemented" % R)
 
         K = R.number_field()
@@ -3914,8 +3913,8 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             ...
             ValueError: P must be prime
         """
-        from sage.rings.number_field.number_field_ideal import is_NumberFieldIdeal
-        if not is_NumberFieldIdeal(P):
+        from sage.rings.number_field.number_field_ideal import NumberFieldIdeal
+        if not isinstance(P, NumberFieldIdeal):
             if isinstance(P, NumberFieldElement):
                 P = self.number_field().fractional_ideal(P)
             else:
diff --git a/src/sage/rings/number_field/number_field_ideal.py b/src/sage/rings/number_field/number_field_ideal.py
index 36e568fbe96..a9f87ae1836 100644
--- a/src/sage/rings/number_field/number_field_ideal.py
+++ b/src/sage/rings/number_field/number_field_ideal.py
@@ -1789,6 +1789,10 @@ def is_NumberFieldIdeal(x):
 
         sage: from sage.rings.number_field.number_field_ideal import is_NumberFieldIdeal
         sage: is_NumberFieldIdeal(2/3)
+        doctest:warning...
+        DeprecationWarning: The function is_NumberFieldIdeal is deprecated;
+        use 'isinstance(..., NumberFieldIdeal)' instead.
+        See https://github.com/sagemath/sage/issues/38124 for details.
         False
         sage: is_NumberFieldIdeal(ideal(5))
         False
@@ -1804,6 +1808,10 @@ def is_NumberFieldIdeal(x):
         sage: is_NumberFieldIdeal(Z)
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38124,
+                "The function is_NumberFieldIdeal is deprecated; "
+                "use 'isinstance(..., NumberFieldIdeal)' instead.")
     return isinstance(x, NumberFieldIdeal)
 
 
@@ -3316,6 +3324,10 @@ def is_NumberFieldFractionalIdeal(x):
 
         sage: from sage.rings.number_field.number_field_ideal import is_NumberFieldFractionalIdeal
         sage: is_NumberFieldFractionalIdeal(2/3)
+        doctest:warning...
+        DeprecationWarning: The function is_NumberFieldFractionalIdeal is deprecated;
+        use 'isinstance(..., NumberFieldFractionalIdeal)' instead.
+        See https://github.com/sagemath/sage/issues/38124 for details.
         False
         sage: is_NumberFieldFractionalIdeal(ideal(5))
         False
@@ -3330,6 +3342,10 @@ def is_NumberFieldFractionalIdeal(x):
         sage: is_NumberFieldFractionalIdeal(Z)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38124,
+                "The function is_NumberFieldFractionalIdeal is deprecated; "
+                "use 'isinstance(..., NumberFieldFractionalIdeal)' instead.")
     return isinstance(x, NumberFieldFractionalIdeal)
 
 
diff --git a/src/sage/rings/number_field/number_field_ideal_rel.py b/src/sage/rings/number_field/number_field_ideal_rel.py
index 7c0e4daa7a2..bb74b64a8e6 100644
--- a/src/sage/rings/number_field/number_field_ideal_rel.py
+++ b/src/sage/rings/number_field/number_field_ideal_rel.py
@@ -891,6 +891,10 @@ def is_NumberFieldFractionalIdeal_rel(x):
         sage: from sage.rings.number_field.number_field_ideal_rel import is_NumberFieldFractionalIdeal_rel
         sage: from sage.rings.number_field.number_field_ideal import is_NumberFieldFractionalIdeal
         sage: is_NumberFieldFractionalIdeal_rel(2/3)
+        doctest:warning...
+        DeprecationWarning: The function is_NumberFieldFractionalIdeal_rel is deprecated;
+        use 'isinstance(..., NumberFieldFractionalIdeal_rel' instead.
+        See https://github.com/sagemath/sage/issues/38124 for details.
         False
         sage: is_NumberFieldFractionalIdeal_rel(ideal(5))
         False
@@ -911,7 +915,9 @@ def is_NumberFieldFractionalIdeal_rel(x):
         Fractional ideal (-a)
         sage: is_NumberFieldFractionalIdeal_rel(N)
         False
-        sage: is_NumberFieldFractionalIdeal(N)
-        True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38124,
+                "The function is_NumberFieldFractionalIdeal_rel is deprecated; "
+                "use 'isinstance(..., NumberFieldFractionalIdeal_rel' instead.")
     return isinstance(x, NumberFieldFractionalIdeal_rel)
diff --git a/src/sage/rings/number_field/number_field_rel.py b/src/sage/rings/number_field/number_field_rel.py
index 7d7c150d9d0..c5e5548f43f 100644
--- a/src/sage/rings/number_field/number_field_rel.py
+++ b/src/sage/rings/number_field/number_field_rel.py
@@ -80,6 +80,7 @@
 from sage.categories.map import is_Map
 from sage.structure.sequence import Sequence
 
+import sage.rings.abc
 import sage.structure.parent_gens
 
 from . import maps
@@ -93,12 +94,12 @@
 
 from . import number_field_element
 import sage.rings.number_field.number_field_ideal_rel
-from .number_field_ideal import is_NumberFieldIdeal
+from .number_field_ideal import NumberFieldIdeal
 from .number_field import (NumberField, NumberField_generic,
     put_natural_embedding_first, proof_flag,
     is_NumberFieldHomsetCodomain)
 from sage.rings.number_field.number_field_base import NumberField as NumberField_base
-from sage.rings.number_field.order import (RelativeOrder, is_NumberFieldOrder,
+from sage.rings.number_field.order import (RelativeOrder,
                                            relative_order_from_ring_generators)
 from sage.rings.number_field.morphism import RelativeNumberFieldHomomorphism_from_abs
 from sage.libs.pari.all import pari_gen
@@ -122,6 +123,10 @@ def is_RelativeNumberField(x):
         sage: from sage.rings.number_field.number_field_rel import is_RelativeNumberField
         sage: x = polygen(ZZ, 'x')
         sage: is_RelativeNumberField(NumberField(x^2+1,'a'))
+        doctest:warning...
+        DeprecationWarning: The function is_RelativeNumberField is deprecated;
+        use 'isinstance(..., NumberField_relative)' instead.
+        See https://github.com/sagemath/sage/issues/38124 for details.
         False
         sage: k.<a> = NumberField(x^3 - 2)
         sage: l.<b> = k.extension(x^3 - 3); l
@@ -131,6 +136,10 @@ def is_RelativeNumberField(x):
         sage: is_RelativeNumberField(QQ)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38124,
+                "The function is_RelativeNumberField is deprecated; "
+                "use 'isinstance(..., NumberField_relative)' instead.")
     return isinstance(x, NumberField_relative)
 
 
@@ -1013,9 +1022,9 @@ def _coerce_map_from_(self, R):
         """
         if R is int:
             return self._generic_coerce_map(R)
-        elif R in (ZZ, QQ, self.base_field()):
+        if R in (ZZ, QQ, self.base_field()):
             return self._generic_coerce_map(R)
-        if is_NumberFieldOrder(R) and R.number_field() is self:
+        if isinstance(R, sage.rings.abc.Order) and R.number_field() is self:
             return self._generic_coerce_map(R)
         mor = self.base_field()._internal_coerce_map_from(R)
         if mor is not None:
@@ -1310,7 +1319,7 @@ def is_isomorphic_relative(self, other, base_isom=None):
             Ring endomorphism of Number Field in z9 with defining polynomial x^6 + x^3 + 1
               Defn: z9 |--> z9^4
         """
-        if is_RelativeNumberField(other):
+        if isinstance(other, NumberField_relative):
             s_base_field = self.base_field()
             o_base_field = other.base_field()
             if base_isom is None:
@@ -2722,7 +2731,7 @@ def uniformizer(self, P, others="positive"):
             sage: (P, 1) in K.factor(u)
             True
         """
-        if not is_NumberFieldIdeal(P):
+        if not isinstance(P, NumberFieldIdeal):
             P = self.ideal(P)
         if not P.is_maximal():
             raise ValueError("P (=%s) must be a nonzero prime." % P)
diff --git a/src/sage/rings/number_field/order.py b/src/sage/rings/number_field/order.py
index 94d0732704d..f5d51d955cf 100644
--- a/src/sage/rings/number_field/order.py
+++ b/src/sage/rings/number_field/order.py
@@ -362,7 +362,11 @@ def is_NumberFieldOrder(R):
 
         sage: from sage.rings.number_field.order import is_NumberFieldOrder
         sage: x = polygen(ZZ, 'x')
-        sage: is_NumberFieldOrder(NumberField(x^2 + 1,'a').maximal_order())
+        sage: is_NumberFieldOrder(NumberField(x^2 + 1, 'a').maximal_order())
+        doctest:warning...
+        DeprecationWarning: The function is_NumberFieldOrder is deprecated;
+        use 'isinstance(..., sage.rings.abc.Order) or ... == ZZ' instead.
+        See https://github.com/sagemath/sage/issues/38124 for details.
         True
         sage: is_NumberFieldOrder(ZZ)
         True
@@ -371,6 +375,10 @@ def is_NumberFieldOrder(R):
         sage: is_NumberFieldOrder(45)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38124,
+                "The function is_NumberFieldOrder is deprecated; "
+                "use 'isinstance(..., sage.rings.abc.Order) or ... == ZZ' instead.")
     return isinstance(R, Order) or R == ZZ
 
 
@@ -2842,7 +2850,7 @@ def absolute_order_from_module_generators(gens,
         raise ValueError("each generator must be integral")
 
     K = gens.universe()
-    if is_NumberFieldOrder(K):
+    if isinstance(K, Order) or K == ZZ:
         K = K.number_field()
     V, from_V, to_V = K.vector_space()
     mod_gens = [to_V(x) for x in gens]
diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
index 7bb968c3121..454dd007f98 100644
--- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
@@ -231,7 +231,6 @@ from sage.rings.integer_ring import is_IntegerRing, ZZ
 from sage.rings.integer cimport Integer
 from sage.rings.number_field.number_field_base cimport NumberField
 
-from sage.rings.number_field.order import is_NumberFieldOrder
 from sage.categories.number_fields import NumberFields
 
 from sage.structure.element import coerce_binop
@@ -5614,7 +5613,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
             return RealField(prec).zero()
 
         K = self.base_ring()
-        if K in NumberFields() or is_NumberFieldOrder(K):
+        if K in NumberFields() or isinstance(K, sage.rings.abc.Order) or K == ZZ:
             f = self
         else:
             raise TypeError("Must be over a Numberfield or a Numberfield Order.")
@@ -5666,7 +5665,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
             prec = 53
 
         K = FractionField(self.base_ring())
-        if K not in NumberFields() or is_NumberFieldOrder(K):
+        if K not in NumberFields() and not isinstance(K, sage.rings.abc.Order) and K != ZZ:
             raise TypeError("must be over a Numberfield or a Numberfield order")
 
         return max([K(c).local_height(v, prec=prec) for c in self.coefficients()])
@@ -5710,7 +5709,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
             1.0
         """
         K = FractionField(self.base_ring())
-        if K not in NumberFields() or is_NumberFieldOrder(K):
+        if K not in NumberFields() and not isinstance(K, sage.rings.abc.Order) and K != ZZ:
             return TypeError("must be over a Numberfield or a Numberfield Order")
 
         if K == QQ:
diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index 67f7f4c95e4..48001e11cb0 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -5841,8 +5841,6 @@ cdef class Polynomial(CommutativePolynomial):
         if self.degree() <= 1:
             return R.fraction_field()
 
-        from sage.rings.number_field.number_field import is_NumberField, NumberField
-
         if is_IntegerRing(R):
             from sage.rings.number_field.number_field import NumberField
             return NumberField(self, names)
diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring_element.py b/src/sage/rings/polynomial/polynomial_quotient_ring_element.py
index 31cf61e3811..f6eb840ff91 100644
--- a/src/sage/rings/polynomial/polynomial_quotient_ring_element.py
+++ b/src/sage/rings/polynomial/polynomial_quotient_ring_element.py
@@ -565,8 +565,8 @@ def field_extension(self, names):
 
         f = R.hom([alpha], F, check=False)
 
-        import sage.rings.number_field.number_field_rel as number_field_rel
-        if number_field_rel.is_RelativeNumberField(F):
+        from sage.rings.number_field.number_field_rel import NumberField_relative
+        if isinstance(F, NumberField_relative):
 
             base_map = F.base_field().hom([R.base_ring().gen()])
             g = F.Hom(R)(x, base_map)
diff --git a/src/sage/schemes/elliptic_curves/ell_local_data.py b/src/sage/schemes/elliptic_curves/ell_local_data.py
index 5375f24cad6..015cba10763 100644
--- a/src/sage/schemes/elliptic_curves/ell_local_data.py
+++ b/src/sage/schemes/elliptic_curves/ell_local_data.py
@@ -100,7 +100,7 @@
 from sage.rings.rational_field import QQ
 from sage.rings.integer_ring import ZZ
 from sage.rings.integer import Integer
-from sage.rings.number_field.number_field_ideal import is_NumberFieldFractionalIdeal
+from sage.rings.number_field.number_field_ideal import NumberFieldFractionalIdeal
 
 from sage.rings.number_field.number_field_base import NumberField
 from sage.rings.ideal import is_Ideal
@@ -1197,7 +1197,7 @@ def check_prime(K, P):
     if not isinstance(K, NumberField):
         raise TypeError("%s is not a number field" % (K,))
 
-    if is_NumberFieldFractionalIdeal(P) or P in K:
+    if isinstance(P, NumberFieldFractionalIdeal) or P in K:
         # if P is an ideal, making sure it is a fractional ideal of K
         P = K.fractional_ideal(P)
         if P.is_prime():
diff --git a/src/sage/schemes/projective/projective_point.py b/src/sage/schemes/projective/projective_point.py
index 10dd6c5efe6..1efc16af934 100644
--- a/src/sage/schemes/projective/projective_point.py
+++ b/src/sage/schemes/projective/projective_point.py
@@ -31,7 +31,7 @@
 _NumberFields = NumberFields()
 from sage.rings.integer_ring import ZZ
 from sage.rings.fraction_field import FractionField
-from sage.rings.number_field.order import is_NumberFieldOrder, Order as NumberFieldOrder
+from sage.rings.number_field.order import Order as NumberFieldOrder
 from sage.rings.qqbar import number_field_elements_from_algebraics
 from sage.rings.quotient_ring import QuotientRing_generic
 from sage.rings.rational_field import QQ
@@ -749,7 +749,7 @@ def global_height(self, prec=None):
         if prec is None:
             prec = 53
         K = self.codomain().base_ring()
-        if K in _NumberFields or is_NumberFieldOrder(K):
+        if K in _NumberFields or isinstance(K, NumberFieldOrder) or K == ZZ:
             P = self
         else:
             try: