Definition:Algebraic Dual

Definition
Let $$R$$ be a commutative ring.

Let $$G$$ be a module over $$R$$.

The $R$-module $$\mathcal L_R \left({G, R}\right)$$ of all linear forms on $$G$$ is usually denoted $$G^*$$ and is called the algebraic dual of $$G$$.

The algebraic dual of $$G^*$$ is denoted $$G^{**}$$.