# Category:Scalar Addition

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This category contains results about **Scalar Addition**.

Definitions specific to this category can be found in **Definitions/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 $V$.

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