Definition:Vector Addition/Module

Definition
Let $\struct {R, +_R, \times_R}$ be a ring.

Let $\struct {G, +_G}$ be an abelian group.

Let $M := \struct {G, +_G, \circ}_R$ be the corresponding module over $R$ (either a left module or a right module).

The group operation $+_G$ on $M$ is known as vector addition on $M$.