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Year 2020, Volume 28, Issue 28, 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, Volume 28, Issue 28, 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).

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Marjan Sheibani ABDOLYOUSEFI This is me (Primary Author)
Women's University of Semnan (Farzanegan)
Iran

Publication Date July 14, 2020
Published in Issue Year 2020, Volume 28, Issue 28

Cite

Bibtex @research article { ieja768269, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {220 - 228}, doi = {10.24330/ieja.768269}, title = {NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES}, key = {cite}, author = {Abdolyousefı, Marjan Sheibani} }
APA Abdolyousefı, M. S. (2020). NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES . International Electronic Journal of Algebra , 28 (28) , 220-228 . DOI: 10.24330/ieja.768269
MLA Abdolyousefı, M. S. "NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES" . International Electronic Journal of Algebra 28 (2020 ): 220-228 <https://dergipark.org.tr/en/pub/ieja/issue/55997/768269>
Chicago Abdolyousefı, M. S. "NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES". International Electronic Journal of Algebra 28 (2020 ): 220-228
RIS TY - JOUR T1 - NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES AU - Marjan SheibaniAbdolyousefı Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768269 DO - 10.24330/ieja.768269 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 220 EP - 228 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768269 UR - https://doi.org/10.24330/ieja.768269 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES %A Marjan Sheibani Abdolyousefı %T NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768269 %U 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
AMA Abdolyousefı M. S. NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES. IEJA. 2020; 28(28): 220-228.
Vancouver Abdolyousefı M. S. NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES. International Electronic Journal of Algebra. 2020; 28(28): 220-228.
IEEE M. S. Abdolyousefı , "NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 220-228, Jul. 2020, doi:10.24330/ieja.768269