diff --git a/src/sage/rings/asymptotic/term_monoid.py b/src/sage/rings/asymptotic/term_monoid.py
index 53dfbc621a1..36b3d2e4f33 100644
--- a/src/sage/rings/asymptotic/term_monoid.py
+++ b/src/sage/rings/asymptotic/term_monoid.py
@@ -1916,7 +1916,7 @@ def _validate_growth_or_error_(self, kwds_construction):
         - ``kwds_construction`` -- a dictionary representing
           the keyword arguments of a term in its construction
           (see also :meth:`GenericTerm.construction` and
-           :meth:`TermWithCoefficient.construction`)
+          :meth:`TermWithCoefficient.construction`)
 
         OUTPUT:
 
@@ -1976,7 +1976,7 @@ def _validate_coefficient_or_error_(self, kwds_construction):
         - ``kwds_construction`` -- a dictionary representing
           the keyword arguments of a term in its construction
           (see also :meth:`GenericTerm.construction` and
-           :meth:`TermWithCoefficient.construction`)
+          :meth:`TermWithCoefficient.construction`)
 
         OUTPUT:
 
@@ -2068,7 +2068,7 @@ def _convert_construction_(self, kwds_construction):
         - ``kwds_construction`` -- a dictionary representing
           the keyword arguments of a term in its construction
           (see also :meth:`GenericTerm.construction` and
-           :meth:`TermWithCoefficient.construction`)
+          :meth:`TermWithCoefficient.construction`)
 
         OUTPUT:
 
@@ -2991,7 +2991,7 @@ def _convert_construction_(self, kwds_construction):
         - ``kwds_construction`` -- a dictionary representing
           the keyword arguments of a term in its construction
           (see also :meth:`GenericTerm.construction` and
-           :meth:`TermWithCoefficient.construction`)
+          :meth:`TermWithCoefficient.construction`)
 
         OUTPUT:
 
@@ -3588,7 +3588,7 @@ def _validate_coefficient_or_error_(self, kwds_construction):
         - ``kwds_construction`` -- a dictionary representing
           the keyword arguments of a term in its construction
           (see also :meth:`GenericTerm.construction` and
-           :meth:`TermWithCoefficient.construction`)
+          :meth:`TermWithCoefficient.construction`)
 
         OUTPUT:
 
@@ -3676,7 +3676,7 @@ def _convert_construction_(self, kwds_construction):
         - ``kwds_construction`` -- a dictionary representing
           the keyword arguments of a term in its construction
           (see also :meth:`GenericTerm.construction` and
-           :meth:`TermWithCoefficient.construction`)
+          :meth:`TermWithCoefficient.construction`)
 
         OUTPUT:
 
@@ -4453,7 +4453,7 @@ def _convert_construction_(self, kwds_construction):
         - ``kwds_construction`` -- a dictionary representing
           the keyword arguments of a term in its construction
           (see also :meth:`GenericTerm.construction` and
-           :meth:`TermWithCoefficient.construction`)
+          :meth:`TermWithCoefficient.construction`)
 
         OUTPUT:
 
@@ -4995,7 +4995,7 @@ def _convert_construction_(self, kwds_construction):
         - ``kwds_construction`` -- a dictionary representing
           the keyword arguments of a term in its construction
           (see also :meth:`GenericTerm.construction` and
-           :meth:`TermWithCoefficient.construction`)
+          :meth:`TermWithCoefficient.construction`)
 
         OUTPUT:
 
diff --git a/src/sage/rings/complex_interval_field.py b/src/sage/rings/complex_interval_field.py
index effc3b60648..f7c9ab64eaf 100644
--- a/src/sage/rings/complex_interval_field.py
+++ b/src/sage/rings/complex_interval_field.py
@@ -12,7 +12,7 @@
 
 - Carl Witty (2007-10-24): rewrite for intervals
 
-- Niles Johnson (2010-08): :Trac:`3893`: ``random_element()``
+- Niles Johnson (2010-08): :trac:`3893`: ``random_element()``
   should pass on ``*args`` and ``**kwds``.
 
 - Travis Scrimshaw (2012-10-18): Added documentation to get full coverage.
diff --git a/src/sage/rings/function_field/place.py b/src/sage/rings/function_field/place.py
index 190d0329efc..a05d9ae3fae 100644
--- a/src/sage/rings/function_field/place.py
+++ b/src/sage/rings/function_field/place.py
@@ -941,7 +941,7 @@ def _residue_field(self, name=None):
 
         def to_V(e):
             """
-            An example to show the idea: Suppose that
+            An example to show the idea: Suppose that::
 
                     [x 0 0]
                 M = [0 1 0] and v = (x^10, x^7 + x^3, x^7 + x^4 + x^3 + 1)
diff --git a/src/sage/rings/number_field/bdd_height.py b/src/sage/rings/number_field/bdd_height.py
index 39ab3ceca09..7e863142524 100644
--- a/src/sage/rings/number_field/bdd_height.py
+++ b/src/sage/rings/number_field/bdd_height.py
@@ -454,14 +454,14 @@ def rational_in(x, y):
 
     def delta_approximation(x, delta):
         r"""
-        Compute a rational number in range (x-delta, x+delta)
+        Compute a rational number in range `(x-delta, x+delta)`
         """
         return rational_in(x - delta, x + delta)
 
     def vector_delta_approximation(v, delta):
         r"""
-        Compute a rational vector w=(w1, ..., wn)
-        such that |vi-wi|<delta for all i in [1, n]
+        Compute a rational vector `w=(w_1, ..., w_n)`
+        such that `|v_i-w_i|<delta` for all `i` in `[1, n]`
         """
         return [delta_approximation(vi, delta) for vi in v]
 
diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index e00dbe9b7d2..912ec22d4b3 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -4207,7 +4207,7 @@ def _pari_absolute_structure(self):
         - ``beta`` is the image of `x \bmod g` under the inverse
           isomorphism `\phi^{-1}\colon K[x]/(g) \to K[x]/(f)`
 
-        EXAMPLES::
+        EXAMPLES:
 
         If `f` is monic and integral, the result satisfies ``g = f``
         and ``alpha = beta = x``::
diff --git a/src/sage/rings/number_field/number_field_rel.py b/src/sage/rings/number_field/number_field_rel.py
index 0a022049f02..77eacd0a3d7 100644
--- a/src/sage/rings/number_field/number_field_rel.py
+++ b/src/sage/rings/number_field/number_field_rel.py
@@ -1529,7 +1529,7 @@ def _pari_relative_structure(self):
         - ``beta`` is the image of `x \bmod g` under the inverse
           isomorphism `\phi^{-1}\colon K[x]/(g) \to K[x]/(f)`.
 
-        EXAMPLES::
+        EXAMPLES:
 
         If the defining polynomials are monic and integral, the result
         satisfies ``g = f`` and ``alpha = beta = x``::
diff --git a/src/sage/rings/number_field/order.py b/src/sage/rings/number_field/order.py
index 8f4d5349505..0bfeefb1da7 100644
--- a/src/sage/rings/number_field/order.py
+++ b/src/sage/rings/number_field/order.py
@@ -1727,7 +1727,7 @@ def _assume_maximal(self, is_maximal=True, p=None):
         Record that this order ``is_maximal`` at the integer prime ``p``.
 
         To support the deprecated behavior for
-        ``is_maximal="non-maximal-non-unique"`, this returns an order.
+        ``is_maximal="non-maximal-non-unique"``, this returns an order.
         Typically, the order itself.
 
         EXAMPLES::
@@ -2319,7 +2319,7 @@ def _assume_maximal(self, is_maximal=True, p=None):
         Record that this order ``is_maximal`` at the integer prime ``p``.
 
         To support the deprecated behavior for
-        ``is_maximal="non-maximal-non-unique"`, this returns an order.
+        ``is_maximal="non-maximal-non-unique"``, this returns an order.
         Typically, the order itself.
 
         EXAMPLES::
diff --git a/src/sage/rings/padics/lattice_precision.py b/src/sage/rings/padics/lattice_precision.py
index a041394d635..6b1386e4121 100644
--- a/src/sage/rings/padics/lattice_precision.py
+++ b/src/sage/rings/padics/lattice_precision.py
@@ -1306,11 +1306,13 @@ def history(self, compact=True, separate_reduce=False, timings=True, output_type
             0.000009s  oo~~o~o~ooo~o~ooo~o~
             0.014250s  oooooooooooo
 
-        The legend is the following::
+        The legend is the following:
+
         - the symbol ``o`` represents a tracked element,
         - the symbol ``~`` represents an element which is marked for deletion.
 
         On the history, we see:
+
         - 1st line: twenty new elements were created
           (this corresponds to the affectation of the list ``L``);
         - 2nd line: elements at prime positions were marked for deletion
@@ -1489,6 +1491,7 @@ def timings(self, action=None):
           a dictionary
 
         Here are the meanings of the keywords above:
+
         - ``add``: time spent in adding new columns to the precision matrix
           (corresponding to the creation of new elements)
         - ``mark``: time spent in marking elements for deletion
diff --git a/src/sage/rings/polynomial/ore_polynomial_ring.py b/src/sage/rings/polynomial/ore_polynomial_ring.py
index 1694eb9289a..0914fcb822b 100644
--- a/src/sage/rings/polynomial/ore_polynomial_ring.py
+++ b/src/sage/rings/polynomial/ore_polynomial_ring.py
@@ -976,7 +976,7 @@ def random_element(self, degree=(-1, 2), monic=False, *args, **kwds):
             (3*t^2 + 1)*x^4 + (4*t + 2)*x^3 + (4*t + 1)*x^2
              + (t^2 + 3*t + 3)*x + 3*t^2 + 2*t + 2
 
-        TESTS::
+        TESTS:
 
         If the first tuple element is greater than the second, a
         ``ValueError`` is raised::
diff --git a/src/sage/rings/tests.py b/src/sage/rings/tests.py
index 4938a3f72e8..56cb05ba256 100644
--- a/src/sage/rings/tests.py
+++ b/src/sage/rings/tests.py
@@ -310,7 +310,8 @@ def test_random_elements(level=MAX_LEVEL, trials=1):
     Create random elements of random rings until a crash occurs, in
     which case an exception is raised.  Defaults to running a single
     trial, but more can be specified.  To run tests in an infinite
-    loop, you could use:
+    loop, you could use::
+
         while True: test_random_elements(trials=100, print_seed=True)
 
     INPUT:
@@ -358,7 +359,8 @@ def test_random_arith(level=MAX_LEVEL, trials=1):
     Create random elements of random rings and does some arithmetic
     with them, until a crash occurs, in which case an exception is
     raised.  Defaults to running a single trial, but more can be
-    specified.  To run tests in an infinite loop, you could use:
+    specified.  To run tests in an infinite loop, you could use::
+
         while True: test_random_arith(trials=100, print_seed=True)
 
     INPUT: