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Been trying to figure this out for a while now (at least a week). The Problem Set was already handed in but I’m still trying to figure this out since I wasn’t able to answer this prior to handing it in. I really want to understand this better. Here’s the problem.

Let $0\to A\to B\to C\to 0$ be a short exact sequence of Modules. If $M$ is any module, prove that there are exact sequences.

$0\to A\oplus M\to B\oplus M\to C\to 0$

and

$0\to A\to B\oplus M\to C\oplus M\to 0$.

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    "Adjoining a direct sum to a short exact sequence" or something similar would be a better title.2012-10-29

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