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Let $R$ be a 2-primal strongly 2-nil-clean ring. We prove that every square matrix over $R$ is the sum of a tripotent and a nilpotent matrices. The similar result for rings of bounded index is proved. We thereby provide a large class of rings over which every matrix is the sum of a tripotent and a nilpotent matrices.
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참고문헌 (17)
참고문헌 신청
A. N. Abyzov / 2017 / On some matrix analogues of the little Fermat theorem / Mat. Zametki 101(2):163~168
S. Breaz / Rings in which every element in either a sum or a difference of a nilpotent and an idempotent / J. Algebra Appl.
S. Breaz / 2013 / Nil clean matrix rings / Linear Algebra Appl. 439:3115~3119
S. Breaz / 2016 / Nil-clean companion matrices / Linear Algebra Appl. 489:50~60
H. Chen / 2011 / Rings related to stable range conditions, Series in Algebra, 11 / World Scientific Publishing Co. Pte. Ltd
S. Breaz / Rings in which every element in either a sum or a difference of a nilpotent and an idempotent / J. Algebra Appl.
S. Breaz / 2013 / Nil clean matrix rings / Linear Algebra Appl. 439:3115~3119
S. Breaz / 2016 / Nil-clean companion matrices / Linear Algebra Appl. 489:50~60
H. Chen / 2011 / Rings related to stable range conditions, Series in Algebra, 11 / World Scientific Publishing Co. Pte. Ltd
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