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 $M$.