Annihilator is Submodule of Algebraic Dual

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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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