Definition:Algebraic Dual

This page is about Algebraic Dual in the context of Linear Algebra. For other uses, see Dual.

Definition

Let $R$ be a commutative ring.

Let $G$ 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 $G$.

Double Dual

The double dual $G^{**}$ of $G$ is the dual of its dual $G^*$.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): $\S 28$