On nilpotent matrices that are unit-regular
DOI:
https://doi.org/10.24193/subbmath.2025.4.02Keywords:
von Neumann regular, nilpotent, matrix, Bezout domain, exchange ring, shift matrix, block diagonal matrixAbstract
In this paper, we characterize regular nilpotent 2 × 2 matrices over Bézout domains and prove that they are unit-regular. We also demonstrate that nilpotent n × n matrices over division rings are unit-regular.
Mathematics Subject Classification (2010): 15B99, 15B33, 16U10, 16U90.
Received 13 August 2025; Accepted 02 October 2025.
References
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[3] Khurana, D., Unit-regularity of regular nilpotent elements. Algebra Represent Theory 19(2016), 641-644.
[4] Nicholson, W.K., Lifting idempotents and exchange rings. Trans. Amer. Math. Soc. 229(1977), 69-278.
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