\begin{definition}[Definition:Scalar Addition/Module]
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 ring addition operation $+_R$ on $M$ is known as '''scalar addition''' on $M$.
Category:Definitions/Module Theory
Category:Definitions/Scalar Addition
\end{definition}