I've been asked to solve the following question:
Given that $e$ is a non-zero idempotent element of a unital ring $R$, show that:
$rad_{J}(eRe) = (eRe)\cap rad_{J}R = e(rad_{J}R)e$.
The strategy I was told to use was by inclusion - show that they're subsets of each other and to also use the fact that $1 - ra$ is invertible for all $r\in R$.
Can anyone give me some steps in the right direction?