Definition:Algebraic Dual

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 $R$.

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 $G$.

Also see

 * Definition:Dual Vector Space