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math.RA2014★ 1 cited
Rings in which every element is either a sum or a difference of a nilpotent and an idempotent
Simion Breaz, Peter Danchev, Yiqiang Zhou
{Generalizing the notion of nil cleanness from \cite{D13}, in parallel to \cite{DM14}, we define the concept of {\it weak nil cleanness} for an arbitrary ring. Its comprehensive st…
math.RA2014
Generalizing pi-regular rings
Peter Danchev, Janez Šter
We introduce the class weakly nil clean rings, as rings R in which for every a\in R there exist an idempotent e and a nilpotent q such that a-e-q\in eRa. Every weakly nil clean rin…