Statement

Let ${\mathbb{K}}$ be a field and $f \in {\mbox{${\mathbb{K}}$}}[x]$ be a univariate polynomial of positive degree $n$ . We denote by ${\mathbb{L}}$ the residue class ring ${\mbox{${\mathbb{K}}$}}[x] / \langle f \rangle$ . Since we do not assume that $f$ is an irreducible polynomial, some non-zero elements in ${\mathbb{L}}$ may not have an inverse. This motivates the following notion. For any $a \in {\mbox{${\mathbb{L}}$}}$ , with $a \neq 0$ , we call quasi-inverse of $a$ , any $b \in {\mbox{${\mathbb{L}}$}}$ , with $b \neq 0$ , such that either $ab = 0$ or $ab = 1$ holds.