On nilpotent matrices that are unit-regular
DOI:
https://doi.org/10.24193/subbmath.2025.4.02Keywords:
Bezout domain, exchange ring, block diagonal matrixAbstract
In this paper, we characterize regular nilpotent 2 x 2 matrices over Bezout domains and prove that they are unit-regular. We also demonstrate that nilpotent n x n matrices over division rings are unit-regular.
References
P. Ara Strongly π-regular rings have stable range one. Proc. A. M. S. 124 (11) (1996), 3293-3298. DOI: https://doi.org/10.1090/S0002-9939-96-03473-9
G. C˘alug˘areanu, Y. Zhou Rings with fine nilpotents. Annali dell Universita di Ferrara 67 (2021), 231-241. DOI: https://doi.org/10.1007/s11565-021-00369-3
D. Khurana Unit-regularity of regular nilpotent elements. Algebra Represent Theory 19 (2016), 641-644. DOI: https://doi.org/10.1007/s10468-015-9592-1
W.K. Nicholson Lifting idempotents and exchange rings. Trans. Amer. Math. Soc. 229 (1977), 69-278. DOI: https://doi.org/10.1090/S0002-9947-1977-0439876-2
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