Definition:Additive Group of Integer Multiples

Definition
Let $n \in \Z_{>0}$.

The additive group $\left({n \Z, +}\right)$ of integer multiples of $n$ is the set of integer multiples of $n$ under the operation of addition.

Also see

 * Integer Multiples under Addition form Infinite Cyclic Group

Thus integer addition is:


 * Well-defined on $n \Z$
 * Closed on $n \Z$
 * Associative on $n \Z$
 * Commutative on $n \Z$
 * The identity of $\left({n \Z, +}\right)$ is $0$
 * Each element of $\left({n \Z, +}\right)$ has an inverse.