Definition:Ring of Integers Modulo m

Definition
Let $m \in \Z: m \ge 2$.

Let $\Z_m$ be the set of integers modulo $m$.

Let $+_m$ and $\times_m$ denote addition modulo $m$ and multiplication modulo $m$ respectively.

The algebraic structure $\left({\Z_m, +_m, \times_m}\right)$ is a commutative ring with unity $\left[\!\left[{1}\right]\!\right]_m$.

The zero of $\left({\Z_m, +_m, \times_m}\right)$ is $\left[\!\left[{0}\right]\!\right]_m$.

Also see

 * Ring of Integers Module m is Ring