On mj-clean ring and strongly mj-clean ring

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Ulucak G., Kör A.

Turkish Journal of Mathematics, vol.46, no.Special Issue 2, pp.2015-2022, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: Special Issue 2
  • Publication Date: 2022
  • Doi Number: 10.55730/1300-0098.3249
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2015-2022
  • Keywords: j-clean ring, strongly j-clean ring, mj-clean ring, strongly mj-clean ring
  • Kocaeli University Affiliated: No

Abstract

© TÜBİTAKIn 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.