\begin{definition}[Definition:Algebraic Dual]
Let $\struct {R, +, \times}$ be a commutative ring.
Let $\struct {G, +_G, \circ}_R$ be an $R$-module.
Let $\struct {R, +_R, \circ}_R$ denote the $R$-module $R$.
The $R$-module $\map {\LL_R} {G, R}$ of all linear forms on $G$ is usually denoted $G^*$ and is called the '''algebraic dual''' of $G$.
\end{definition}