# Semisimple rings with a unique maximal ideals

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1. Oct 27, 2014

### mahler1

1. The problem statement, all variables and given/known data
Determine all semisimple rings with a unique maximal ideal.

3. The attempt at a solution

If I call $I$ to the unique maximal ideal of $R$, then $I$ can be seen as a simple $R$-submodule, by hypothesis, there exists $I' \subset R$, $R-$submodule such that $R=I \bigoplus I'$. I got stuck at this point, any suggestions would be appreciated.

2. Nov 1, 2014