Annihilator is Submodule of Algebraic Dual/Corollary

Theorem
Let $R$ be a commutative ring with unity.

Let $G$ be a module over $R$.

Let $M$ be a submodule of $G$.

Let $G^*$ be the algebraic dual of $G$.

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
Follows directly as an example of Annihilator is Submodule of Algebraic Dual.