Communications of the Korean Mathematical Society (대한수학회논문집)

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INVO-CLEAN UNITAL RINGS

  • Danchev, Peter V. (Department of Mathematics Plovdiv University)
  • Received : 2016.03.15
  • Published : 2017.01.31
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Abstract

We define and completely describe the structure of invo-clean rings having identity. We show that these rings are clean but not (weakly) nil-clean and thus they possess independent properties than these obtained by Diesl in [7] and by Breaz-Danchev-Zhou in [2].

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References

  1. M.-S. Ahn and D. D. Anderson, Weakly clean rings and almost clean rings, Rocky Mount. J. Math. 36 (2006), no. 3, 783-798. https://doi.org/10.1216/rmjm/1181069429
  2. S. Breaz, P. Danchev, and Y. Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl. 15 (2016), no. 8, 1650148, 11 pp.
  3. A. Cimpean and P. Danchev, Weakly nil-clean index and uniquely weakly nil-clean rings, Internat. Electr. J. Algebra 21 (2017).
  4. P. V. Danchev, Weakly UU rings, Tsukuba J. Math. 40 (2016), 101-118. https://doi.org/10.21099/tkbjm/1474747489
  5. P. V. Danchev and T. Y. Lam, Rings with unipotent units, Publ. Math. (Debrecen) 88 (2016), 449-466. https://doi.org/10.5486/PMD.2016.7405
  6. P. V. Danchev and W. Wm. McGovern, Commutative weakly nil clean unital rings, J. Algebra 425 (2015), 410-422. https://doi.org/10.1016/j.jalgebra.2014.12.003
  7. A. J. Diesl, Nil clean rings, J. Algebra 383 (2013), 197-211. https://doi.org/10.1016/j.jalgebra.2013.02.020
  8. N. Jacobson, Structure theory for algebraic algebras of bounded degree, Ann. of Math. 46 (1945), 695-707. https://doi.org/10.2307/1969205
  9. W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269-278. https://doi.org/10.1090/S0002-9947-1977-0439876-2
  10. W. K. Nicholson and Y. Zhou, Rings in which elements are uniquely the sum of an idempotent and a unit, Glasg. Math. J. 46 (2004), no. 2, 227-236. https://doi.org/10.1017/S0017089504001727
  11. J. Ster, Nil-clean involutions, arXiv preprint, 2015.

Cited by

  1. Weakly invo-clean unital rings 2017, https://doi.org/10.1007/s13370-017-0515-7
  2. A Generalization of WUU Rings vol.69, pp.10, 2018, https://doi.org/10.1007/s11253-018-1460-9