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Rings generalized by tripotents and nilpotents

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Abstract

We present new characterizations of the rings for which every element is a sum of two tripotents and a nilpotent that commute. These extend the results of Z. L. Ying, M. T. Koşan, Y. Zhou (2016) and Y. Zhou (2018).

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References

  1. A. N. Abyzov: Strongly q-nil-clean rings. Sib. Math. J. 60 (2019), 197–208.

    Article  MathSciNet  MATH  Google Scholar 

  2. H. Chen: Rings Related Stable Range Conditions. Series in Algebra 11. World Scientific, Hackensack, 2011.

    Book  MATH  Google Scholar 

  3. H. Chen, M. Sheibani: Strongly 2-nil-clean rings. J. Algebra Appl. 16 (2017), Article ID 1750178, 12 pages.

  4. P. V. Danchev, T.-Y. Lam: Rings with unipotent units. Publ. Math. 88 (2016), 449–466.

    MathSciNet  MATH  Google Scholar 

  5. A. J. Diesl: Nil clean rings. J. Algebra 383 (2013), 197–211.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. T. Koşan, Z. Wang, Y. Zhou: Nil-clean and strongly nil-clean rings. J. Pure Appl. Algebra 220 (2016), 633–646.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. T. Koşan, T. Yildirim, Y. Zhou: Rings whose elements are the sum of a tripotent and an element from the Jacobson radical. Can. Math. Bull. 62 (2019), 810–821.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. T. Koşan, T. Yildirim, Y. Zhou: Rings with xn− x nilpotent. J. Algebra Appl. 19 (2020), Article ID 2050065, 14 pages.

  9. Z. Ying, M. T. Koşan, Y. Zhou: Rings in which every element is a sum of two tripotents. Can. Math. Bull. 59 (2016), 661–672.

    Article  MathSciNet  MATH  Google Scholar 

  10. Y. Zhou: Rings in which elements are sums of nilpotents, idempotents and tripotents. J. Algebra Appl. 17 (2018), Article ID 1850009, 7 pages.

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Authors and Affiliations

  1. School of Mathematics, Hangzhou Normal University, Yuhangtang Road, Yuhang District, Zhejiang, 311121, Hangzhou, P. R. China

    Huanyin Chen

  2. Farzanegan Campus, Semnan University, Semnan, Iran

    Marjan Sheibani

  3. Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

    Nahid Ashrafi

Authors
  1. Huanyin Chen
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  2. Marjan Sheibani
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  3. Nahid Ashrafi
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Corresponding author

Correspondence to Marjan Sheibani.

Additional information

The research has been supported by the Natural Science Foundation of Zhejiang Province, China (No. LY21A010018).

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Chen, H., Sheibani, M. & Ashrafi, N. Rings generalized by tripotents and nilpotents. Czech Math J 72, 1175–1182 (2022). https://doi.org/10.21136/CMJ.2022.0427-21

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  • DOI: https://doi.org/10.21136/CMJ.2022.0427-21

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