Definition:Algebraic Dual
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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): $\S 28$