I'm curious about it. I know that if $M=A\oplus B$ then $M/A \cong B$ (identifying $A$ with $A\oplus 0$), one would expect that the "converse" holds, i.e., if $M/A\cong B$ then $M\cong A\oplus B$. Is it true in general? (Assume $R$ is an integral domain).
2026-05-05 13:41:39.1777988499
Under what conditions $M \cong (M/N) \oplus N$ where $M$ is an $R-$module and $N$ is a submodule?
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No, Let $M=R=\mathbb{Z}$, $N=2\mathbb{Z}$