Maximal Annihilator of Module is Associated Prime
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Theorem
Let $A$ be a commutative ring with unity.
Let $M$ be a module over $A$.
Let $\mathbf p$ be a maximal element of the set:
- $\set { \map {\operatorname {Ann}_A} x : x \in M , x \ne 0 }$
with respect to the subset relation.
Then $\mathfrak p$ is an associated prime of $M$.
Proof
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