Category:Scalar Multiplication

This category contains results about Scalar Multiplication.
Definitions specific to this category can be found in Definitions/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.