Local idempotents in a von Neumann regular rings

Question

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

Answer 1

In a von Neumann regular ring, local idempotents are those idempotents $e$ such that $Re$ is a field. In particular, it is also a minimal ideal.