Annihilator is Submodule of Algebraic Dual
From ProofWiki
Theorem
Let $R$ be a commutative ring.
Let $G$ be a module over $R$.
Let $M$ be a submodule of $G$.
Let $G^*$ be the algebraic dual of $G$.
Then the annihilator $M^\circ$ of $M$ is a submodule of $G^*$.
Similarly, let $N$ be a submodule of $G^*$.
Let $G^{**}$ be the algebraic dual of $G^*$.
Then the annihilator $N^\circ$ of $N$ is a submodule of $G^{**}$.
Proof
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Sources
- Seth Warner: Modern Algebra (1965): $\S 28$
