It is known by Brauer Lemma that every minimal left ideal $I$ of a ring $R$ is either nilpotent (in fact $I^2=0$) or $I=Re$, where $e^2=e\in R$. Is it true that the sum of two minimal left ideals $Re$ and $Rf$ each generated by idempotents $e$ and $f$ is again generated by an idempotent? In von Neuman regular rings it is the case. Maybe it is so when the intersection of these is zero!
Any help would be appreciated!