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 \( 𝔽_{3} \) 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 \( |F|-1 \).
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Funding
This work was supported by the Volga Region Research and Education Center of Mathematics (Project No. 075–02–2020–1478).
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Abyzov, A.N., Tapkin, D.T. Rings over Which Matrices Are Sums of Idempotent and \( q \)-Potent Matrices. Sib Math J 62, 1–13 (2021). https://doi.org/10.1134/S0037446621010018
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DOI: https://doi.org/10.1134/S0037446621010018