Definition:Scalar Ring/Unitary Module

Definition
Let $\struct {G, +_G, \circ}_R$ be a module, where:


 * $\struct {R, +_R, \times_R}$ is a ring with unity


 * $\struct {G, +_G}$ is an abelian group


 * $\circ: R \times G \to G$ is a binary operation.

Then the ring $\struct {R, +_R, \times_R}$ is called the scalar ring of $\struct {G, +_G, \circ}_R$.

If the scalar ring is understood, then $\struct {G, +_G, \circ}_R$ can be rendered $\struct {G, +_G, \circ}$.

Also see

 * Definition:Scalar Ring of Module