Given a finite ring $A$ which is a free left module over a subring $R$ of
$A$, two types of $R$-bases, pseudo-self-dual bases (similar to trace
orthogonal bases) and symmetric bases, are defined which in turn are used to
define duality preserving maps from codes over $A$ to codes over $R$. Both
types of bases are generalizations of similar concepts for fields. Many
illustrative examples are given to shed light on the advantages to such
mappings as well as their abundance

Szabo, Steve