Definition:Scalar Multiplication/R-Algebraic Structure

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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.