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Year 2020, , 220 - 228, 14.07.2020
https://doi.org/10.24330/ieja.768269

Abstract

References

  • P. Danchev, Strongly nil-clean corner rings, Bull. Iranian Math. Soc., 43 (2017), 1333-1339.
  • M. T. Kosan, Z. Wang and Y. Zhou, Nil-clean and strongly nil-clean rings, J. Pure Appl. Algebra, 220 (2016), 633-646.
  • G. T. Marks, 2-Primal Rings, Ph.D. Thesis, University of California, Berkeley, 2000.
  • M. Sheibani Abdolyousefi, N. Ashrafi and H. Chen, On Zhou nil-clean rings, arXiv:1705.05094 [math.RA], (2017).
  • M. Sheibani Abdolyousefi and H. Chen, Matrices over Zhou nil-clean rings, Comm. Algebra, 46 (2018), 1527-1533.
  • Z. Ying, M. T. Kosan and Y. Zhou, Rings in which every element is a sum of two tripotents, Canad. Math. Bull., 59 (2016), 661-672.
  • Y. Zhou, Rings in which elements are sums of nilpotents, idempotents and tripotents, J. Algebra Appl., 17 (2018), 1850009 (7 pp).

NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES

Year 2020, , 220 - 228, 14.07.2020
https://doi.org/10.24330/ieja.768269

Abstract

A ring $R$ is Zhou nil-clean if every element in $R$ is the sum of a nilpotent and two tripotents. Let $R$ be a Zhou nil-clean ring. If $R$ is of bounded index or 2-primal, we prove that every square matrix over $R$ is the sum of a nilpotent and a linear combination of two idempotents. This provides a large class of rings over which every square matrix has such decompositions by nilpotent and linear combination of idempotent matrices. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

References

  • P. Danchev, Strongly nil-clean corner rings, Bull. Iranian Math. Soc., 43 (2017), 1333-1339.
  • M. T. Kosan, Z. Wang and Y. Zhou, Nil-clean and strongly nil-clean rings, J. Pure Appl. Algebra, 220 (2016), 633-646.
  • G. T. Marks, 2-Primal Rings, Ph.D. Thesis, University of California, Berkeley, 2000.
  • M. Sheibani Abdolyousefi, N. Ashrafi and H. Chen, On Zhou nil-clean rings, arXiv:1705.05094 [math.RA], (2017).
  • M. Sheibani Abdolyousefi and H. Chen, Matrices over Zhou nil-clean rings, Comm. Algebra, 46 (2018), 1527-1533.
  • Z. Ying, M. T. Kosan and Y. Zhou, Rings in which every element is a sum of two tripotents, Canad. Math. Bull., 59 (2016), 661-672.
  • Y. Zhou, Rings in which elements are sums of nilpotents, idempotents and tripotents, J. Algebra Appl., 17 (2018), 1850009 (7 pp).
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Marjan Sheibani Abdolyousefı This is me

Publication Date July 14, 2020
Published in Issue Year 2020

Cite

APA Abdolyousefı, M. S. (2020). NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES. International Electronic Journal of Algebra, 28(28), 220-228. https://doi.org/10.24330/ieja.768269
AMA Abdolyousefı MS. NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES. IEJA. July 2020;28(28):220-228. doi:10.24330/ieja.768269
Chicago Abdolyousefı, Marjan Sheibani. “NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES”. International Electronic Journal of Algebra 28, no. 28 (July 2020): 220-28. https://doi.org/10.24330/ieja.768269.
EndNote Abdolyousefı MS (July 1, 2020) NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES. International Electronic Journal of Algebra 28 28 220–228.
IEEE M. S. Abdolyousefı, “NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES”, IEJA, vol. 28, no. 28, pp. 220–228, 2020, doi: 10.24330/ieja.768269.
ISNAD Abdolyousefı, Marjan Sheibani. “NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES”. International Electronic Journal of Algebra 28/28 (July 2020), 220-228. https://doi.org/10.24330/ieja.768269.
JAMA Abdolyousefı MS. NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES. IEJA. 2020;28:220–228.
MLA Abdolyousefı, Marjan Sheibani. “NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES”. International Electronic Journal of Algebra, vol. 28, no. 28, 2020, pp. 220-8, doi:10.24330/ieja.768269.
Vancouver Abdolyousefı MS. NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES. IEJA. 2020;28(28):220-8.