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This article is cited in 5 scientific papers (total in 5 papers)
Rings over which matrices are sums of idempotent and $q$-potent matrices
A. N. Abyzov, D. T. Tapkin Kazan (Volga Region) Federal University, Kazan, Russia
Abstract:
We study the rings over which each square matrix is the sum of an idempotent matrix
and a $q$-potent matrix. We also show that if $F$ is a finite field not isomorphic to $\Bbb{F}_3$ and
$q>1$ is odd then each square matrix over $F$ is the sum of an idempotent matrix
and a $q$-potent matrix if and only if $q-1$ is divisible by $| F | -1$.
Keywords:
idempotent, $q$-potent, Frobenius normal form.
Received: 11.05.2020 Revised: 01.06.2020 Accepted: 17.06.2020
Citation:
A. N. Abyzov, D. T. Tapkin, “Rings over which matrices are sums of idempotent and $q$-potent matrices”, Sibirsk. Mat. Zh., 62:1 (2021), 3–18; Siberian Math. J., 62:1 (2021), 1–13
Linking options:
https://www.mathnet.ru/eng/smj7533 https://www.mathnet.ru/eng/smj/v62/i1/p3
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Abstract page: | 253 | Full-text PDF : | 75 | References: | 38 | First page: | 11 |
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