Definition:Linear Form

Definition
Let $\struct {R, +, \times}$ be a commutative ring.

Let $\struct {R, +_R, \circ}_R$ denote the $R$-module $R$.

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 $R$.

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

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

Also see

 * Definition:Algebraic Dual
 * Definition:Bilinear Form