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\geq 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.
ULUCAK, GÜLŞEN and KÖR, ARDA
"On $ mj $-clean ring and strongly $ mj $-clean ring,"
Turkish Journal of Mathematics: Vol. 46:
5, Article 28.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss5/28