Definition:Vector Addition/Module
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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 $M$.