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.
$ j $-clean ring, strongly $ j $-clean ring, $ mj $-clean ring, strongly $ mj $-clean ring
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