Integers Modulo m under Addition form Abelian Group

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Theorem

Let $\Z_m$ is the set of integers modulo $m$

Let $+_m$ be the operation of addition modulo $m$.

Then the structure $\struct {\Z_m, +_m}$ is an abelian group.


Proof

From Integers Modulo m under Addition form Cyclic Group, $\struct {\Z_m, +_m}$ is a cyclic group.

The result follows from Cyclic Group is Abelian.

$\blacksquare$


Sources

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