Definition:Additive Group of Integers Modulo m

Definition
Let $m \in \Z$ such that $m > 1$.

The additive group of integers modulo $m$, denoted $\struct {\Z_m, +_m}$, is the set of integers modulo $m$ under the operation of addition modulo $m$.

Also denoted as
Some sources denote $\struct {\Z_m, +_m}$ as $\struct {\N_m, +_m}$, defining the underlying set as a subset of the natural numbers rather than the integers:


 * $\N_m = \set {0, 1, \ldots, m - 1}$

As can be seen, $\Z_m$ and $\N_m$ are the same thing.

Also see

 * Integers Modulo m under Addition form Cyclic Group