Definition:Scalar/Module

This page is about Scalar in the context of Module Theory. For other uses, see Scalar.

Definition

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

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

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

The elements of the scalar ring $\struct {R, +_R, \times_R}$ are called scalars.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 26$. Vector Spaces and Modules
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Module