diff --git a/src/qldpc/objects.py b/src/qldpc/objects.py
index 369b1c1cd..f380b30f0 100644
--- a/src/qldpc/objects.py
+++ b/src/qldpc/objects.py
@@ -57,7 +57,7 @@ def swap_xz(self) -> PauliXZ:
         if self is Pauli.Z:
             return Pauli.X
         raise ValueError(
-            f"Pauli.dual_xz only converts between Pauli.X and Pauli.Z (provided: {self})"
+            f"Pauli.swap_xz only converts between Pauli.X and Pauli.Z (provided: {self})"
         )
 
     def __str__(self) -> str:
@@ -144,10 +144,10 @@ def from_string(string: str) -> QuditPauli:
             raise ValueError(invalid_op)
 
         for factor in factors:
-            pauli = factor[0]
+            pauli = factor[:1]
             val_str = factor[2:-1]
             _factor = f"{pauli}({val_str})"
-            if pauli not in "XYZ" or not val_str.isnumeric() or factor != _factor:
+            if pauli not in "XYZ" or not val_str.isdecimal() or factor != _factor:
                 raise ValueError(invalid_op)
 
             val = int(val_str)
@@ -172,9 +172,6 @@ class Node:
     index: int
     is_data: bool = True
 
-    def __hash__(self) -> int:
-        return hash((self.index, self.is_data))
-
     def __lt__(self, other: Node) -> bool:
         if self.is_data == other.is_data:
             return self.index < other.index
@@ -267,9 +264,6 @@ class CayleyComplex:
     subset_b: set[abstract.GroupMember]
     bipartite: bool
 
-    # geometric data
-    _graph: nx.Graph | None = None
-
     def __init__(
         self,
         subset_a: Collection[abstract.GroupMember],
@@ -396,8 +390,7 @@ class ChainComplex:
     _field: type[galois.FieldArray]
     _ops: tuple[npt.NDArray[np.int_] | abstract.RingArray, ...]
 
-    # if boundary operators are defined over a group algebra, keep track of the base group and ring
-    _group: abstract.Group | None
+    # if boundary operators are defined over a group algebra, keep track of the base ring
     _ring: abstract.GroupRing | None
 
     def __init__(
@@ -435,7 +428,7 @@ def __init__(
             self._validate_ops()
 
     def _validate_ops(self) -> None:
-        """Validate the consistency of this the boundary operators in this chain complex."""
+        """Validate the consistency of the boundary operators in this chain complex."""
         for op_a, op_b in zip(self.ops, self.ops[1:]):
             if op_a.shape[1] != op_b.shape[0] or np.any(op_a @ op_b):
                 raise ValueError(
@@ -574,9 +567,6 @@ def get_zero_block(
 
         if chain_a.ring is None:
             return ChainComplex([op.view(chain_field) for op in matrices], skip_validation=True)
-        ops = []
-        for matrix in matrices:
-            op = matrix.view(abstract.RingArray)
-            op._ring = chain_a.ring
-            ops.append(op)
+        # rebuild each operator through RingArray.build to coerce every entry into a ring member
+        ops = [abstract.RingArray.build(matrix, chain_a.ring) for matrix in matrices]
         return ChainComplex(ops, skip_validation=True)
diff --git a/src/qldpc/objects_test.py b/src/qldpc/objects_test.py
index f473ac58f..f3e728bdc 100644
--- a/src/qldpc/objects_test.py
+++ b/src/qldpc/objects_test.py
@@ -56,7 +56,7 @@ def test_qudit_operator() -> None:
     assert -objects.QuditPauli((0, 1)) == objects.QuditPauli((0, -1))
     for op in ["I", "Y(1)", "X(1)*Z(2)"]:
         assert str(objects.QuditPauli.from_string(op)) == op
-    for op in ["a*b*c", "a(1)"]:
+    for op in ["a*b*c", "a(1)", "*", "X(1)*", "", "X(²)"]:
         with pytest.raises(ValueError, match="Invalid qudit operator"):
             objects.QuditPauli.from_string(op)
 
@@ -137,6 +137,19 @@ def test_chain_complex(field: int = 3) -> None:
     assert not np.any(two_chain.op(0))
     assert not np.any(two_chain.op(two_chain.num_links + 1))
 
+    # a tensor product over a nontrivial commutative group algebra must yield boundary operators
+    # whose entries are all ring members (and can therefore be lifted to matrices), including the
+    # three-or-more-link case where some operator blocks are entirely zero
+    cyclic_ring = abstract.GroupRing(abstract.CyclicGroup(3), field)
+    cyclic_matrix = abstract.RingArray.build(matrix, cyclic_ring)
+    ring_chain = objects.ChainComplex.tensor_product(cyclic_matrix, cyclic_matrix)
+    ring_chain = objects.ChainComplex.tensor_product(ring_chain, cyclic_matrix)
+    ring_chain._validate_ops()
+    for ring_op in ring_chain.ops:
+        # every op of a ring-valued chain is a RingArray; assert narrows the union type for .lift()
+        assert isinstance(ring_op, abstract.RingArray)
+        ring_op.lift()
+
     # invalid chain complex constructions
     with pytest.raises(ValueError, match="inconsistent operator types"):
         objects.ChainComplex([matrix, abstract.RingArray.build([[0]])])