3
$\begingroup$

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?

  • 0
    You should try merging your accounts.2011-12-24

1 Answers 1

2

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

  • 1
    The first volume of the book by Assem, Skowroński and Simson on representation theory. The first couple of chapters, in fact.2011-12-24