Geodesic
Rings, matrices over which are representable as the sum of two potent matrices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2023), pp. 90-94

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This paper investigates conditions under which representability of each element $a$ from the field $P$ as the sum $a= f+g$, with $f^{q_{1}} = f$, $g^{q_{2}} = g$ and $q_1, q_2$ are fixed integers $>1$, implies a similar representability of each square matrix over the field $P$. We propose a general approach to solving this problem. As an application we describe fields and commutative rings with $2$ is a unit, over which each square matrix is the sum of two $4$-potent matrices.
Mots-clés : $q$-potent
Keywords: finite field, matrices over finite fields. 
@article{IVM_2023_12_a6,
     author = {A. N. Abyzov and D. T. Tapkin},
     title = {Rings, matrices over which are representable as the sum of two potent matrices},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {90--94},
     publisher = {mathdoc},
     number = {12},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_12_a6/}
}
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A. N. Abyzov; D. T. Tapkin. Rings, matrices over which are representable as the sum of two potent matrices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2023), pp. 90-94. http://geodesic.mathdoc.fr/item/IVM_2023_12_a6/