On mj-clean ring and strongly mj-clean ring

Abstract

In this paper, we introduce the concepts of mj-clean and strongly mj-clean rings which are generalizations of j-clean ring and strongly j-clean ring, respectively. Let R be a ring with a nonzero identity and m >= 2 a positive integer. We call the ring R as mj-clean if each element of R can be written as a sum of an m-potent and an element of J(R) and also if these elements are commute, then we call R as strongly mj-clean ring. We examine the algebraic properties of these new concepts and show the effects of these structures on matrix rings, polynomial rings, power series and the transitions between them.