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Let $N$ be a submodule of the module $M$. Suppose $M/N$ and $N$ are semi-simple. Does it follow that $M$ is semi-simple?

I think the answer is yes but I am not sure how to prove it. Any help would be appreciated.

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    No. In fact this is false even if you assume that $M/N$ and $N$ are simple, and even for a ring as well-behaved as $\mathbb{Z}$.2012-05-15

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