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3 hours ago comment added Jason Starr No, that is not true. Let $A$ be $\mathbb{C}[[s,t]/\langle st \rangle$, let $M$ be $A/\langle s \rangle$, and let $N$ be $A/\langle t \rangle$. Then $\text{Hom}_A(M,N)$ is the zero module.
5 hours ago history asked Naga Venkata CC BY-SA 4.0