Generalizing nil clean rings

Abstract

We introduce the class of {\it unipotently nil clean} rings as these rings $R$ in which for every $a\in R$ there exist an idempotent $e$ and a nilpotent $q$ such that $a-e-1-q\in (1-e)Ra$. Each unipotently nil clean ring is weakly nil clean as well as each nil clean ring is unipotently nil clean. Our results obtained here considerably extend those from [8] and [7], respectively.