A Generalization Of Regular And Strongly $\Pi$-regular Rings

Abstract

We introduce and investigate the so-called D-regularly nil clean rings by showing that these rings are, in fact, a non-trivial generalization of the classical von Neumann regular rings and of the strongly $\pi$-regular rings. Some other close relationships with certain well-known classes of rings such as $\pi$-regular rings, exchange rings, clean rings, nil-clean rings, etc., are also demonstrated. These results somewhat supply a recent publication of the author in Turk. J. Math. (2019) as well as they somewhat expand the important role of the two examples of nil-clean rings obtained by Ster in Lin. Algebra \& Appl. (2018). Likewise, the obtained symmetrization supports that for exchange rings established by Khurana et al. in Algebras \& Represent. Theory (2015).