A generalization of π-regular rings

Abstract

We introduce the class of so-called regularly nil clean rings and systematically study their fundamentalcharacteristic properties accomplished with relationships among certain classical sorts of rings such as exchange rings,Utumi rings etc. These rings of ours naturally generalize the long-known classes of π-regular and strongly π-regularrings. We show that the regular nil cleanness possesses a symmetrization which extends the corresponding one forstrong π -regularity that was visualized by Dischinger [10]. Likewise, our achieved results substantially improve onestablishments presented in two recent papers by Danchev and Šter [8] and Danchev [6].