  Let $\E$ be a commutative ring with identity and $P\in\E[x]$ be a polynomial.
In the present paper we consider digit representations in the residue class
ring $\E[x]/(P)$. In particular, we are interested in the question whether each
$A\in\E[x]/(P)$ can be represented modulo $P$ in the form $e_0+e_1 X + \cdots +
e_h X^h$, where the $e_i\in\E[x]/(P)$ are taken from a fixed finite set of
digits. This general concept generalises both canonical number systems and
digit systems over finite fields. Due to the fact that we do not assume that
$0$ is an element of the digit set and that $P$ need not be monic, several new
phenomena occur in this context.
