Consider the short exact sequence of modules
$$0\rightarrow M\rightarrow N\rightarrow K\rightarrow0$$ Let $K$ be an Artinian (Noetherian) module, can we get $N$ is an Artinian (Noetherian) module?
2026-03-27 08:38:42.1774600722
Artinian module and short exact sequence
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The result, as concerns short exact sequences, is that $N$ is artinian if and only if $M$ and $K$ are artinian.