Definition:Scalar/R-Algebraic Structure

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


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

$\struct {S, *_1, *_2, \ldots, *_n}$ is an algebraic structure with $n$ operations
$\struct {R, +_R, \times_R}$ is the scalar ring of $\struct {S, *_1, *_2, \ldots, *_n, \circ}_R$.

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