# Artinian module and short exact sequence

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?

• $K$ could be the zero module, and $M \cong N$, so it seems you'll need more assumptions than this. – mollyerin Jan 13 '15 at 22:31

The result, as concerns short exact sequences, is that $N$ is artinian if and only if $M$ and $K$ are artinian.