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.

$\blacksquare$

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 28$. Linear Transformations