Lifting of $n$-potents

Question

Let $n$ be a positive integer. An element $e$ in a ring $R$ is called $n$-potent if $e^n=e$. I want a reference investigating lifting $n$-potents modulo $J(R)$, the Jacobson radical of $R$. By lifting we mean if $x^n-x\in J(R)$ then there exists an $n$-potent $e\in R$ such that $x-e\in J(R)$. Thanks in advance!