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.

• Results about Additive Groups of Integer Multiples can be found here.