# Is a ring with the following properties semiprime? (Part 2)

Let $R$ be a ring with $1 \neq 0$ that contains noncentral idempotents. If for every noncentral idempotent $e$ of $R$ the corner ring $eRe$ is a division ring and $eR(1-e)Re \neq 0$, is the ring $R$ semiprime?

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You should try merging your accounts. –  user667648 Dec 24 '11 at 2:08

If you modify my example by modding out by all paths of length $3$ you get a counterexample.