diff --git a/src/sage/algebras/free_algebra.py b/src/sage/algebras/free_algebra.py
index 382ce536827..2c6f99367c7 100644
--- a/src/sage/algebras/free_algebra.py
+++ b/src/sage/algebras/free_algebra.py
@@ -159,7 +159,6 @@
 #                  https://www.gnu.org/licenses/
 # ***************************************************************************
 
-
 from sage.algebras.free_algebra_element import FreeAlgebraElement
 from sage.categories.algebras_with_basis import AlgebrasWithBasis
 from sage.categories.functor import Functor
@@ -376,34 +375,6 @@ def create_object(self, version, key):
 FreeAlgebra = FreeAlgebraFactory('FreeAlgebra')
 
 
-def is_FreeAlgebra(x) -> bool:
-    """
-    Return ``True`` if x is a free algebra; otherwise, return ``False``.
-
-    EXAMPLES::
-
-        sage: from sage.algebras.free_algebra import is_FreeAlgebra
-        sage: is_FreeAlgebra(5)
-        doctest:warning...
-        DeprecationWarning: the function is_FreeAlgebra is deprecated;
-        use 'isinstance(..., (FreeAlgebra_generic, FreeAlgebra_letterplace))' instead
-        See https://github.com/sagemath/sage/issues/37896 for details.
-        False
-        sage: is_FreeAlgebra(ZZ)
-        False
-        sage: is_FreeAlgebra(FreeAlgebra(ZZ,100,'x'))
-        True
-        sage: is_FreeAlgebra(FreeAlgebra(ZZ,10,'x',implementation='letterplace'))
-        True
-        sage: is_FreeAlgebra(FreeAlgebra(ZZ,10,'x',implementation='letterplace',
-        ....:                            degrees=list(range(1,11))))
-        True
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(37896, "the function is_FreeAlgebra is deprecated; use 'isinstance(..., (FreeAlgebra_generic, FreeAlgebra_letterplace))' instead")
-    return isinstance(x, (FreeAlgebra_generic, FreeAlgebra_letterplace))
-
-
 class FreeAlgebra_generic(CombinatorialFreeModule):
     """
     The free algebra on `n` generators over a base ring.
@@ -470,7 +441,7 @@ class FreeAlgebra_generic(CombinatorialFreeModule):
     """
     Element = FreeAlgebraElement
 
-    def __init__(self, R, n, names, degrees=None):
+    def __init__(self, R, n, names, degrees=None) -> None:
         """
         The free algebra on `n` generators over a base ring.
 
diff --git a/src/sage/algebras/free_algebra_quotient_element.py b/src/sage/algebras/free_algebra_quotient_element.py
index 6c1857e5363..5f35031f0a5 100644
--- a/src/sage/algebras/free_algebra_quotient_element.py
+++ b/src/sage/algebras/free_algebra_quotient_element.py
@@ -3,11 +3,11 @@
 Free algebra quotient elements
 
 AUTHORS:
-    - William Stein (2011-11-19): improved doctest coverage to 100%
-    - David Kohel (2005-09): initial version
-"""
 
-#*****************************************************************************
+- William Stein (2011-11-19): improved doctest coverage to 100%
+- David Kohel (2005-09): initial version
+"""
+# ***************************************************************************
 #  Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
@@ -19,9 +19,8 @@
 #  See the GNU General Public License for more details; the full text
 #  is available at:
 #
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
-
+#                  https://www.gnu.org/licenses/
+# ***************************************************************************
 from sage.misc.repr import repr_lincomb
 from sage.structure.element import RingElement, AlgebraElement
 from sage.structure.parent_gens import localvars
@@ -32,34 +31,8 @@
 from sage.algebras.free_algebra_element import FreeAlgebraElement
 
 
-def is_FreeAlgebraQuotientElement(x):
-    """
-    EXAMPLES::
-
-        sage: H, (i,j,k) = sage.algebras.free_algebra_quotient.hamilton_quatalg(QQ)
-        sage: sage.algebras.free_algebra_quotient_element.is_FreeAlgebraQuotientElement(i)
-        doctest:warning...
-        DeprecationWarning: The function is_FreeAlgebraQuotientElement is deprecated;
-        use 'isinstance(..., FreeAlgebraQuotientElement)' instead.
-        See https://github.com/sagemath/sage/issues/38184 for details.
-        True
-
-    Of course this is testing the data type::
-
-        sage: sage.algebras.free_algebra_quotient_element.is_FreeAlgebraQuotientElement(1)
-        False
-        sage: sage.algebras.free_algebra_quotient_element.is_FreeAlgebraQuotientElement(H(1))
-        True
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(38184,
-                "The function is_FreeAlgebraQuotientElement is deprecated; "
-                "use 'isinstance(..., FreeAlgebraQuotientElement)' instead.")
-    return isinstance(x, FreeAlgebraQuotientElement)
-
-
 class FreeAlgebraQuotientElement(AlgebraElement):
-    def __init__(self, A, x):
+    def __init__(self, A, x) -> None:
         """
         Create the element x of the FreeAlgebraQuotient A.
 
diff --git a/src/sage/algebras/quatalg/quaternion_algebra.py b/src/sage/algebras/quatalg/quaternion_algebra.py
index 7c0b0b287b7..5b531aacab3 100644
--- a/src/sage/algebras/quatalg/quaternion_algebra.py
+++ b/src/sage/algebras/quatalg/quaternion_algebra.py
@@ -459,28 +459,8 @@ def create_object(self, version, key, **extra_args):
 ########################################################
 
 
-def is_QuaternionAlgebra(A):
-    """
-    Return ``True`` if ``A`` is of the QuaternionAlgebra data type.
-
-    EXAMPLES::
-
-        sage: sage.algebras.quatalg.quaternion_algebra.is_QuaternionAlgebra(QuaternionAlgebra(QQ,-1,-1))
-        doctest:warning...
-        DeprecationWarning: the function is_QuaternionAlgebra is deprecated;
-        use 'isinstance(..., QuaternionAlgebra_abstract)' instead
-        See https://github.com/sagemath/sage/issues/37896 for details.
-        True
-        sage: sage.algebras.quatalg.quaternion_algebra.is_QuaternionAlgebra(ZZ)
-        False
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(37896, "the function is_QuaternionAlgebra is deprecated; use 'isinstance(..., QuaternionAlgebra_abstract)' instead")
-    return isinstance(A, QuaternionAlgebra_abstract)
-
-
 class QuaternionAlgebra_abstract(Parent):
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         EXAMPLES::
 
@@ -489,7 +469,7 @@ def _repr_(self):
         """
         return "Quaternion Algebra with base ring %s" % self.base_ring()
 
-    def ngens(self):
+    def ngens(self) -> int:
         """
         Return the number of generators of the quaternion algebra as a K-vector
         space, not including 1.