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Fields over which matrices can be represented as the sum of potent and nilpotent matrices
https://doi.org/10.26907/0021-3446-2025-10-78-82
Abstract
We study fields over which every matrix can be represented as a sum of two potent matrices and a nilpotent matrix. In particular, it is shown that over a field P every matrix can be represented as a sum of two idempotent matrices and a nilpotent matrix exactly when either P = F2, or P = F3.
About the Authors
A. N. Abyzov
Kazan Federal University;
Emperor Alexander I St. Petersburg State Transport University
Russian Federation
Russian Federation
Adel N. Abyzov
18 Kremlyovskaya str., Kazan, 420008,
9 Moskovsky Ave., Saint Petersburg, 190031
D. T. Tapkin
Kazan Federal University;
Emperor Alexander I St. Petersburg State Transport University
Russian Federation
Russian Federation
Danil T. Tapkin
18 Kremlyovskaya str., Kazan, 420008,
9 Moskovsky Ave., Saint Petersburg, 190031
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Review
For citations:
Abyzov A.N., Tapkin D.T. Fields over which matrices can be represented as the sum of potent and nilpotent matrices. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(10):78-82. (In Russ.) https://doi.org/10.26907/0021-3446-2025-10-78-82
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