Let $R$ be a ring and $M,N$ two $R$-modules such that there exists a non-zero map $\psi : M \to N$. Is it true that there exists a non-zero map $\varphi: N \to M$ ?
I do not have any particular restriction on $R$. Thanks for any comment and remark!
2026-05-06 09:43:43.1778060623
Non-zero maps between modules
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Consider $R=\mathbb Z$, $M=\mathbb Z$ and $N=\mathbb Z/2\mathbb Z$.