Basic_Results_about_Unitary_Modules

Let $\struct {G, +_G}$ be an abelian group whose identity is $e$. Let $\struct {R, +_R, \times_R}$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$. Let $\struct {G, +_G, \circ}_R$ be an unitary $R$-module. Let $x \in G, n \in \Z$. Then