Generalizações de anéis regulares e anéis nil limpos

Abstract

In this work, we will talk about regular rings, strongly regular rings, π-regular rings, strongly π-regular rings, clean rings and nil clean rings. The regular elements were defined in 1936 by von Neumann. In 1939, McCoy generalized these elements and defined the π-regular elements. In 1954, Azumaya defined the strongly π-regular elements and in 1977 Nicholson defined the clean rings. In the last years, with the study of clean rings, has emerged the class of nil clean rings, formulated by Diesl. As a consequence of this study, we present properties of these ring classes and how they are related.