\begin{definition}[Definition:Linear Form]
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 $G$'''.
\end{definition}