# Spooky algebra

Let $A$ be a commutative ring, $I, J\subseteq A$ ideals. If $A/I \simeq A/J$ as $A$-modules, then $I=J$.

## One thought on “Spooky algebra”

1. $\mathrm{Ann}(A/I)=I$ and annihilators are preserved by isomorphisms of $A$-modules.

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