# Category:Definitions/Scalar Multiplication

This category contains definitions related to Scalar Multiplication.
Related results can be found in Category:Scalar Multiplication.

### $R$-Algebraic Structure

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.

### Module

Let $\struct {G, +_G, \circ}_R$ be an module (either a left module or a right module or both), where:

$\struct {R, +_R, \times_R}$ is a ring
$\struct {G, +_G}$ is an abelian group.

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

### Vector Space

Let $\struct {G, +_G, \circ}_K$ be a vector space, where:

$\struct {K, +_K, \times_K}$ is a field
$\struct {G, +_G}$ is an abelian group.

The operation $\circ: K \times G \to G$ is called scalar multiplication.

## Pages in category "Definitions/Scalar Multiplication"

The following 14 pages are in this category, out of 14 total.