Basic Results about Unitary Modules

Theorem
Let $\left({G, +_G}\right)$ be an abelian group whose identity is $e$.

Let $\left({R, +_R, \times_R}\right)$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.

Let $\left({G, +_G, \circ}\right)_R$ be an unitary $R$-module.

Let $x \in G, n \in \Z$.

Then:

Also see

 * Basic Results about Modules