# Definition:Linear Form

## 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.