Definition:Scalar Multiplication/R-Algebraic Structure

Definition

Let $\struct {S, *_1, *_2, \ldots, *_n, \circ}_R$ be an $R$-algebraic structure with $n$ operations, where:

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

$\struct {S, *_1, *_2, \ldots, *_n}$ is an algebraic structure with $n$ operations

The operation $\circ: R \times S \to S$ is called scalar multiplication.

Also known as

Some sources refer to scalar multiplication as exterior multiplication.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 26$. Vector Spaces and Modules