Category:Definitions/Algebraic Duals

This category contains definitions related to Algebraic Duals.
Related results can be found in Category:Algebraic Duals.

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 $G$.