# Definition:Linear Form

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## Contents

## Definition

Let $R$ be a commutative ring.

Let $\struct {G, +_G, \circ}_R$ be a module over $R$.

Let $\phi: \struct {G, +_G, \circ}_R \to \struct {R, +_R, \circ}_R$ be a linear transformation from $G$ to the $R$-module $R$.

Then $\phi$ is called a **linear form on $G$**.

## Also known as

A **linear form** is also known as a **linear functional**.

## Also see

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 28$