# Category:Definitions/Scalar Addition

Jump to navigation
Jump to search

This category contains definitions related to Scalar Addition.

Related results can be found in Category:Scalar Addition.

### Scalar Addition on Module

Let $\struct {R, +_R, \times_R}$ be a ring.

Let $\struct {G, +_G}$ be an abelian group.

Let $M := \struct {G, +_G, \circ}_R$ be the corresponding **module over $R$** (either a left module or a right module).

The ring addition operation $+_R$ on $M$ is known as **scalar addition** on $M$.

### Scalar Addition on Vector Space

Let $\struct {K, +_K, \times_K}$ be a field.

Let $\struct {G, +_G}$ be an abelian group.

Let $V := \struct {G, +_G, \circ}_K$ be the corresponding **vector space over $K$**.

The field addition operation $+_K$ on $V$ is known as **scalar addition** on $V$.

## Pages in category "Definitions/Scalar Addition"

The following 5 pages are in this category, out of 5 total.