Annihilator is Submodule of Algebraic Dual/Corollary
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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