Let $R$ be a commutative ring with identity. Recall that an idempotent element $e$ of $R$ is an element a such that $e^2=e$, and a local idempotent is an idempotent a such that $Re$ is a local ring. Also, a von Neumann regular ring is a ring $R$ such that for every $a$ in $R$ there exists an $x$ in $R$ such that $a = axa$.
I am looking for a characterization of local idempotents in a von Neumann regular ring.
Any hint is appreciated