Definition:Additive Group of Integers Modulo m/Also denoted as

Additive Group of Integers Modulo $m$: Also denoted as

The additive group of integers modulo $m$ is denoted by some sources as $\struct {\N_m, +_m}$.

Hence this defines 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.