diff --git a/src/sage/algebras/cluster_algebra.py b/src/sage/algebras/cluster_algebra.py
index c0fa68d27dd..9ee99179fbf 100644
--- a/src/sage/algebras/cluster_algebra.py
+++ b/src/sage/algebras/cluster_algebra.py
@@ -1988,8 +1988,7 @@ def F_polynomial(self, g_vector):
                 msg += "you can compute it by mutating from the initial seed along the sequence "
                 msg += str(self._path_dict[g_vector])
                 raise KeyError(msg)
-            else:
-                raise KeyError("the g-vector %s has not been found yet" % str(g_vector))
+            raise KeyError("the g-vector {} has not been found yet".format(g_vector))
 
     def find_g_vector(self, g_vector, depth=infinity):
         r"""
diff --git a/src/sage/algebras/commutative_dga.py b/src/sage/algebras/commutative_dga.py
index 7dadae0de4d..67ccd766b5d 100644
--- a/src/sage/algebras/commutative_dga.py
+++ b/src/sage/algebras/commutative_dga.py
@@ -1286,8 +1286,7 @@ def _element_constructor_(self, x, coerce=True):
 
         if isinstance(x, sage.interfaces.abc.SingularElement):
             # self._singular_().set_ring()
-            x = self.element_class(self, x.sage_poly(self.cover_ring()))
-            return x
+            return self.element_class(self, x.sage_poly(self.cover_ring()))
 
         return self.element_class(self, x)
 
diff --git a/src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.py b/src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.py
index 677b77fb45c..869fb65791b 100644
--- a/src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.py
+++ b/src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.py
@@ -749,8 +749,7 @@ def one(self):
         """
         if not self.is_unitary():
             raise TypeError("algebra is not unitary")
-        else:
-            return self(self._one)
+        return self(self._one)
 
     def random_element(self, *args, **kwargs):
         """
diff --git a/src/sage/algebras/finite_gca.py b/src/sage/algebras/finite_gca.py
index d488d79e921..de0d849aa36 100644
--- a/src/sage/algebras/finite_gca.py
+++ b/src/sage/algebras/finite_gca.py
@@ -160,8 +160,7 @@ def __classcall_private__(cls, base, names=None, degrees=None,
         if names is None:
             if degrees is None:
                 raise ValueError("you must specify names or degrees")
-            else:
-                n = len(degrees)
+            n = len(degrees)
             names = tuple(f'x{i}' for i in range(n))
         elif isinstance(names, str):
             names = tuple(names.split(','))
@@ -397,13 +396,13 @@ def _repr_term(self, w) -> str:
             return '1'
         # Non-trivial case:
         terms = []
-        for i in range(len(w)):
-            if w[i] == 0:
+        for i, wi in enumerate(w):
+            if wi == 0:
                 continue
-            elif w[i] == 1:
+            if wi == 1:
                 terms.append(self._names[i])
             else:
-                terms.append(self._names[i] + f'^{w[i]}')
+                terms.append(self._names[i] + f'^{wi}')
         return self._mul_symbol.join(terms)
 
     def _latex_term(self, w) -> str:
@@ -432,13 +431,13 @@ def _latex_term(self, w) -> str:
             return '1'
         # Non-trivial case:
         terms = []
-        for i in range(len(w)):
-            if w[i] == 0:
+        for i, wi in enumerate(w):
+            if wi == 0:
                 continue
-            elif w[i] == 1:
+            if wi == 1:
                 terms.append(self._names[i])
             else:
-                terms.append(self._names[i] + '^{' + str(w[i]) + '}')
+                terms.append(self._names[i] + '^{' + str(wi) + '}')
         latex_mul = self._mul_latex_symbol + ' '  # add whitespace
         return latex_mul.join(terms)
 
diff --git a/src/sage/algebras/free_algebra_element.py b/src/sage/algebras/free_algebra_element.py
index db8880eb262..c8443afb5dc 100644
--- a/src/sage/algebras/free_algebra_element.py
+++ b/src/sage/algebras/free_algebra_element.py
@@ -82,7 +82,7 @@ def __init__(self, A, x):
 
         IndexedFreeModuleElement.__init__(self, A, x)
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         Return string representation of ``self``.
 
@@ -104,10 +104,9 @@ def _repr_(self):
         M = P.monoid()
         from sage.structure.parent_gens import localvars
         with localvars(M, P.variable_names(), normalize=False):
-            x = repr_lincomb(v, strip_one=True)
-        return x
+            return repr_lincomb(v, strip_one=True)
 
-    def _latex_(self):
+    def _latex_(self) -> str:
         r"""
         Return latex representation of ``self``.
 
diff --git a/src/sage/algebras/fusion_rings/f_matrix.py b/src/sage/algebras/fusion_rings/f_matrix.py
index e48a89fc664..0549df5754e 100644
--- a/src/sage/algebras/fusion_rings/f_matrix.py
+++ b/src/sage/algebras/fusion_rings/f_matrix.py
@@ -1379,12 +1379,9 @@ def _map_triv_reduce(self, mapper, input_iter, worker_pool=None, chunksize=None,
         else:
             mapped = worker_pool.imap_unordered(executor, input_iter, chunksize=chunksize)
         # Reduce phase
-        results = set()
-        for child_eqns in mapped:
-            if child_eqns is not None:
-                results.update(child_eqns)
-        results = list(results)
-        return results
+        results = {eqn for child_eqns in mapped for eqn in child_eqns
+                   if child_eqns is not None}
+        return list(results)
 
     ########################
     #   Equations set up   #
@@ -1770,8 +1767,7 @@ def _par_graph_gb(self, eqns=None, term_order='degrevlex', largest_comp=45, verb
                 small_comps.append(comp_eqns)
         input_iter = zip_longest(small_comps, [], fillvalue=term_order)
         small_comp_gb = self._map_triv_reduce('compute_gb', input_iter, worker_pool=self.pool, chunksize=1, mp_thresh=50)
-        ret = small_comp_gb + temp_eqns
-        return ret
+        return small_comp_gb + temp_eqns
 
     def _get_component_variety(self, var, eqns):
         r"""
@@ -2324,7 +2320,7 @@ def find_cyclotomic_solution(self, equations=None, algorithm='', verbose=True, o
             []
         """
         if self._poly_ring.ngens() == 0:
-            return
+            return None
         self._reset_solver_state()
         self._var_to_sextuple = {self._poly_ring.gen(i): s for i, s in self._idx_to_sextuple.items()}
 
diff --git a/src/sage/algebras/fusion_rings/fusion_double.py b/src/sage/algebras/fusion_rings/fusion_double.py
index 8376547a7f7..dcf1f11c134 100644
--- a/src/sage/algebras/fusion_rings/fusion_double.py
+++ b/src/sage/algebras/fusion_rings/fusion_double.py
@@ -328,9 +328,9 @@ def s_matrix(self, unitary=False, base_coercion=True):
             [ 1/3  1/3 -1/3    0    0 -1/3  2/3 -1/3]
         """
         b = self.basis()
-        S = matrix([[self.s_ij(b[x], b[y], unitary=unitary, base_coercion=base_coercion)
-                     for x in self.get_order()] for y in self.get_order()])
-        return S
+        return matrix([[self.s_ij(b[x], b[y], unitary=unitary,
+                                  base_coercion=base_coercion)
+                        for x in self.get_order()] for y in self.get_order()])
 
     @cached_method
     def N_ijk(self, i, j, k):
diff --git a/src/sage/algebras/hecke_algebras/cubic_hecke_algebra.py b/src/sage/algebras/hecke_algebras/cubic_hecke_algebra.py
index ecb9551561f..3ed81d81f13 100644
--- a/src/sage/algebras/hecke_algebras/cubic_hecke_algebra.py
+++ b/src/sage/algebras/hecke_algebras/cubic_hecke_algebra.py
@@ -1552,8 +1552,6 @@ def product_on_basis(self, g1, g2):
         g1 = self.monomial(g1)
         g2 = self.monomial(g2)
 
-        result = None
-
         g1_Tietze = g1.Tietze()
         g2_Tietze = g2.Tietze()
 
@@ -1563,9 +1561,8 @@ def product_on_basis(self, g1, g2):
         # The product is calculated from the corresponding product of the braids
         # ----------------------------------------------------------------------
         braid_group = self.braid_group()
-        braid_product = braid_group(g1_Tietze+g2_Tietze)
-        result = self._braid_image(braid_product)
-        return result
+        braid_product = braid_group(g1_Tietze + g2_Tietze)
+        return self._braid_image(braid_product)
 
     ############################################################################
     # --------------------------------------------------------------------------
@@ -2043,8 +2040,7 @@ def _braid_image_from_reduced_powers(self, braid_tietze):
                 return self.one()
             k = braid_tietze[0]*len_braid
             result_vect = self._reduce_gen_power(k)
-            result = self.from_vector(result_vect)
-            return result
+            return self.from_vector(result_vect)
 
         # ----------------------------------------------------------------------
         # Try to use former calculations (from dynamic library) to obtain the
@@ -2094,8 +2090,7 @@ def _braid_image_from_reduced_powers(self, braid_tietze):
                 braid_preimage = tuple(word_result)
             result_vect = self._mult_by_regular_rep(vect, tuple(word_right), RepresentationType.RegularRight, braid_preimage)
 
-        result = self.from_vector(result_vect)
-        return result
+        return self.from_vector(result_vect)
 
     # --------------------------------------------------------------------------
     # _braid_image_from_former_calculations
@@ -2649,7 +2644,6 @@ def _extend_braid_automorphism(self, element, braid_automorphism):
             sage: CHA2.mirror_isomorphism(br)   # indirect doctest
             c^-1
         """
-
         result = self.zero()
         for braid in element.support():
             autom_braid = braid_automorphism(braid)
diff --git a/src/sage/algebras/hecke_algebras/cubic_hecke_base_ring.py b/src/sage/algebras/hecke_algebras/cubic_hecke_base_ring.py
index 98bda5f8c69..7f713844e3f 100644
--- a/src/sage/algebras/hecke_algebras/cubic_hecke_base_ring.py
+++ b/src/sage/algebras/hecke_algebras/cubic_hecke_base_ring.py
@@ -273,7 +273,7 @@ def construction(self):
             sage: ER = chbr.CubicHeckeExtensionRing('a, b, c')
             sage: ER._test_category()   # indirect doctest
         """
-        return None
+        return
 
     def __reduce__(self):
         r"""
diff --git a/src/sage/algebras/hecke_algebras/cubic_hecke_matrix_rep.py b/src/sage/algebras/hecke_algebras/cubic_hecke_matrix_rep.py
index 59b0767fb48..9b12b49eecb 100644
--- a/src/sage/algebras/hecke_algebras/cubic_hecke_matrix_rep.py
+++ b/src/sage/algebras/hecke_algebras/cubic_hecke_matrix_rep.py
@@ -708,7 +708,7 @@ def construction(self):
             sage: MS = c1.matrix().parent()
             sage: MS._test_category()   # indirect doctest
         """
-        return None
+        return
 
     def __reduce__(self):
         r"""
@@ -894,8 +894,8 @@ def invert_gen(matr):
             matri += cf2 * matr
             matri += cf3 * matr**2
             d1, d2 = matr.dimensions()
-            matrI = matrix(original_base_ring, d1, d2, lambda i, j: original_base_ring(matri[i, j]))
-            return matrI
+            return matrix(original_base_ring, d1, d2,
+                          lambda i, j: original_base_ring(matri[i, j]))
 
         if n == 2:
             if representation_type.is_split():
diff --git a/src/sage/algebras/lie_algebras/center_uea.py b/src/sage/algebras/lie_algebras/center_uea.py
index 2799356a4c4..87a21ed3a26 100644
--- a/src/sage/algebras/lie_algebras/center_uea.py
+++ b/src/sage/algebras/lie_algebras/center_uea.py
@@ -225,8 +225,7 @@ def some_elements(self):
         ret = set(gens)
         ret.update([self.prod(gens), gens[1] * gens[3]**4, gens[1]**4 * gens[2]**3])
         # Sort the output for uniqueness
-        ret = sorted(ret, key=lambda m: (self.degree(m), m.to_word_list()))
-        return ret
+        return sorted(ret, key=lambda m: (self.degree(m), m.to_word_list()))
 
     def degree(self, m):
         r"""
diff --git a/src/sage/algebras/lie_algebras/free_lie_algebra.py b/src/sage/algebras/lie_algebras/free_lie_algebra.py
index 08462de239b..4cc9cfada9a 100644
--- a/src/sage/algebras/lie_algebras/free_lie_algebra.py
+++ b/src/sage/algebras/lie_algebras/free_lie_algebra.py
@@ -632,9 +632,9 @@ def _rewrite_bracket(self, l, r):
             for m, inner_coeff in self._rewrite_bracket(l, r._right).items():
                 if r._left == m:
                     continue
-                elif r._left < m:
+                if r._left < m:
                     x, y = r._left, m
-                else: # r._left > m
+                else:  # r._left > m
                     x, y = m, r._left
                     inner_coeff = -inner_coeff
                 for b_elt, coeff in self._rewrite_bracket(x, y).items():
@@ -644,9 +644,9 @@ def _rewrite_bracket(self, l, r):
             for m, inner_coeff in self._rewrite_bracket(l, r._left).items():
                 if m == r._right:
                     continue
-                elif m < r._right:
+                if m < r._right:
                     x, y = m, r._right
-                else: # m > r._right
+                else:  # m > r._right
                     x, y = r._right, m
                     inner_coeff = -inner_coeff
                 for b_elt, coeff in self._rewrite_bracket(x, y).items():
@@ -739,9 +739,9 @@ def _rewrite_bracket(self, l, r):
             for m, inner_coeff in self._rewrite_bracket(l._right, r).items():
                 if l._left == m:
                     continue
-                elif l._left < m:
+                if l._left < m:
                     x, y = l._left, m
-                else: # l._left > m
+                else:  # l._left > m
                     x, y = m, l._left
                     inner_coeff = -inner_coeff
                 for b_elt, coeff in self._rewrite_bracket(x, y).items():
@@ -751,9 +751,9 @@ def _rewrite_bracket(self, l, r):
             for m, inner_coeff in self._rewrite_bracket(l._left, r).items():
                 if m == l._right:
                     continue
-                elif m < l._right:
+                if m < l._right:
                     x, y = m, l._right
-                else: # m > l._right
+                else:  # m > l._right
                     x, y = l._right, m
                     inner_coeff = -inner_coeff
                 for b_elt, coeff in self._rewrite_bracket(x, y).items():
diff --git a/src/sage/algebras/lie_algebras/verma_module.py b/src/sage/algebras/lie_algebras/verma_module.py
index 0e4cdff3732..3ff90671d5c 100644
--- a/src/sage/algebras/lie_algebras/verma_module.py
+++ b/src/sage/algebras/lie_algebras/verma_module.py
@@ -818,12 +818,12 @@ def _acted_upon_(self, scalar, self_on_left=False):
             for m in ret._monomial_coefficients:
                 c = ret._monomial_coefficients[m]
                 mp = {}
-                for k,e in reversed(m._sorted_items()):
+                for k, e in reversed(m._sorted_items()):
                     part = P._g._part_on_basis(k)
                     if part > 0:
                         mp = None
                         break
-                    elif part == 0:
+                    if part == 0:
                         c *= P._g._weight_action(k, P._weight)**e
                     else:
                         mp[k] = e
diff --git a/src/sage/algebras/orlik_solomon.py b/src/sage/algebras/orlik_solomon.py
index f1b46ca4c65..cc8a6b6634c 100644
--- a/src/sage/algebras/orlik_solomon.py
+++ b/src/sage/algebras/orlik_solomon.py
@@ -827,7 +827,7 @@ def construction(self):
             sage: OS1.construction() is None
             True
         """
-        return None
+        return
 
     def _basis_action(self, g, f):
         r"""
diff --git a/src/sage/algebras/orlik_terao.py b/src/sage/algebras/orlik_terao.py
index b039e7bef3f..57bf6bdfb67 100644
--- a/src/sage/algebras/orlik_terao.py
+++ b/src/sage/algebras/orlik_terao.py
@@ -693,7 +693,7 @@ def construction(self):
             sage: OTG.construction() is None
             True
         """
-        return None
+        return
 
     def _basis_action(self, g, f):
         r"""
diff --git a/src/sage/algebras/quantum_matrix_coordinate_algebra.py b/src/sage/algebras/quantum_matrix_coordinate_algebra.py
index c0bff39501e..dbd65339b5c 100644
--- a/src/sage/algebras/quantum_matrix_coordinate_algebra.py
+++ b/src/sage/algebras/quantum_matrix_coordinate_algebra.py
@@ -282,7 +282,7 @@ def product_on_basis(self, a, b):
                 if ax[0] < bx[0]:
                     # In order, so nothing more to do
                     break
-                elif ax[0] == bx[0]:
+                if ax[0] == bx[0]:
                     if ax[1] > bx[1]:
                         # x_{it} x_{ij} = q^{-1} x_{ij} x_{it} if t < j
                         coeff *= qi ** (ae * be)
diff --git a/src/sage/algebras/schur_algebra.py b/src/sage/algebras/schur_algebra.py
index b967064e565..a9000747fba 100644
--- a/src/sage/algebras/schur_algebra.py
+++ b/src/sage/algebras/schur_algebra.py
@@ -456,7 +456,7 @@ def construction(self):
             sage: T = SchurTensorModule(QQ, 2, 3)
             sage: T.construction()
         """
-        return None
+        return
 
     def _monomial_product(self, xi, v):
         """
diff --git a/src/sage/algebras/steenrod/steenrod_algebra.py b/src/sage/algebras/steenrod/steenrod_algebra.py
index 5c3bd7a1fc3..c866d420529 100644
--- a/src/sage/algebras/steenrod/steenrod_algebra.py
+++ b/src/sage/algebras/steenrod/steenrod_algebra.py
@@ -517,7 +517,7 @@ def __classcall__(self, p=2, basis='milnor', **kwds):
         return super().__classcall__(self, p=p, basis=std_basis, profile=std_profile,
                                      truncation_type=std_type, generic=std_generic)
 
-    def __init__(self, p=2, basis='milnor', **kwds):
+    def __init__(self, p=2, basis='milnor', **kwds) -> None:
         r"""
         INPUT:
 
@@ -692,7 +692,7 @@ def prime(self):
         """
         return self._prime
 
-    def basis_name(self):
+    def basis_name(self) -> str:
         r"""
         The basis name associated to ``self``.
 
@@ -707,7 +707,7 @@ def basis_name(self):
         """
         return self.prefix()
 
-    def _has_nontrivial_profile(self):
+    def _has_nontrivial_profile(self) -> bool:
         r"""
         Return ``True`` if the profile function for this algebra seems to be that
         for a proper sub-Hopf algebra of the Steenrod algebra.
@@ -744,7 +744,7 @@ def _has_nontrivial_profile(self):
                   or (profile[1] and min(profile[1]) == 1)))
                 or (trunc < Infinity))
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         Printed representation of the Steenrod algebra.
 
@@ -799,7 +799,7 @@ def abridge_list(l):
             return "sub-Hopf algebra of %smod %d Steenrod algebra, %s basis, profile function %s" % (genprefix, self.prime(), self._basis_name, pro_str)
         return "%smod %d Steenrod algebra, %s basis" % (genprefix, self.prime(), self._basis_name)
 
-    def _latex_(self):
+    def _latex_(self) -> str:
         r"""
         LaTeX representation of the Steenrod algebra.
 
@@ -813,7 +813,7 @@ def _latex_(self):
         """
         return "\\mathcal{A}_{%s}" % self.prime()
 
-    def _repr_term(self, t):
+    def _repr_term(self, t) -> str:
         r"""
         String representation of the monomial specified by the tuple ``t``.
 
@@ -901,10 +901,9 @@ def _repr_term(self, t):
             s = comm_long_mono_to_string(t, p, generic=self._generic)
         elif basis.find('comm') >= 0:
             s = comm_mono_to_string(t, generic=self._generic)
-        s = s.replace('{', '').replace('}', '')
-        return s
+        return s.replace('{', '').replace('}', '')
 
-    def _latex_term(self, t):
+    def _latex_term(self, t) -> str:
         r"""
         LaTeX representation of the monomial specified by the tuple ``t``.
 
@@ -949,8 +948,7 @@ def _latex_term(self, t):
         s = s.replace("Sq", "\\text{Sq}")
         if not self.basis_name().find('pst') >= 0:
             s = s.replace("P", "\\mathcal{P}")
-        s = s.replace("beta", "\\beta")
-        return s
+        return s.replace("beta", "\\beta")
 
     def profile(self, i, component=0):
         r"""
@@ -2403,22 +2401,20 @@ def Q_exp(self, *nums):
         if not all(x in (0, 1) for x in nums):
             raise ValueError("the tuple %s should consist " % (nums,) +
                              "only of 0s and 1s")
-        else:
-            if self.basis_name() != 'milnor':
-                return self(SteenrodAlgebra(p=self.prime(),
-                                            generic=self._generic).Q_exp(*nums))
-            while nums[-1] == 0:
-                nums = nums[:-1]
-            if not self._generic:
-                return self.P(*nums)
-            else:
-                mono = ()
-                index = 0
-                for e in nums:
-                    if e == 1:
-                        mono = mono + (index,)
-                    index += 1
-                return self.Q(*mono)
+
+        if self.basis_name() != 'milnor':
+            return self(SteenrodAlgebra(p=self.prime(),
+                                        generic=self._generic).Q_exp(*nums))
+
+        lnums = list(nums)
+        while lnums[-1] == 0:
+            lnums.pop()
+
+        if not self._generic:
+            return self.P(*lnums)
+
+        mono = (index for index, e in enumerate(lnums) if e == 1)
+        return self.Q(*mono)
 
     def Q(self, *nums):
         r"""