Category:Definitions/Scalar Addition

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 $V$.