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Rings in which every element is a sum of a nilpotent and three tripotents

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In this article, we completely determine the rings for which every element is a sum of a nilpotent and three tripotents that commute with one another. We discuss this property for some extensions of rings, including group rings.

Abstract

In this article, we completely determine the rings for which every element is a sum of a nilpotent and three tripotents that commute with one another. We discuss this property for some extensions of rings, including group rings.

참고문헌 (9)

  1. Huanyin Chen, "Strongly 2-nil-clean rings", Journal of Algebra and Its Applications, 16(09), pp.1750178~ (2017), World Scientific Pub Co Pte Lt[DOI]
  2. I. G. Connell, "On the group ring", Canadian J. Math, 15, pp.650~685 (1963)[DOI]
  3. Alexander J. Diesl, "Nil clean rings", Journal of Algebra, 383, pp.197~211 (2013), Elsevier BV[DOI]
  4. Yasuyuki Hirano, "Rings in which every element is the sum of two idempotents", Bulletin of the Australian Mathematical Society, 37(2), pp.161~164 (1988), Cambridge University Press (CUP)[DOI]
  5. Y. Hirano, "On rings in which every element is uniquely expressible as a sum of a nilpotent element and a certain potent element", Math. J. Okayama Univ, 30, pp.33~40 (1988)
  6. Tamer Koşan, "Nil-clean and strongly nil-clean rings", Journal of Pure and Applied Algebra, 220(2), pp.633~646 (2016), Elsevier BV[DOI]
  7. J. Levitzki, "On the structure of algebraic algebras and related rings", Trans. Amer. Math. Soc, 74, pp.384~409 (1953)[DOI]
  8. Zhiling Ying, "Rings in which Every Element is a Sum of Two Tripotents", Canadian Mathematical Bulletin, 59(3), pp.661~672 (2016), Canadian Mathematical Society[DOI]
  9. Yiqiang Zhou, "Rings in which elements are sums of nilpotents, idempotents and tripotents", Journal of Algebra and Its Applications, 17(01), pp.1850009~ (2018), World Scientific Pub Co Pte Lt[DOI]

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