Geodesic
On Some Matrix Analogs of the Little Fermat Theorem
Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 163-168

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The rings over which every square matrix is representable as a sum of a nilpotent matrix and a $q$-potent matrix, where $q$ is a positive integer power of a prime, are studied. As consequences, matrix analogs of the little Fermat theorem are obtained.
Keywords: nil clean rings, regular rings, little Fermat theorem. 
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     author = {A. N. Abyzov and I. I. Mukhametgaliev},
     title = {On {Some} {Matrix} {Analogs} of the {Little} {Fermat} {Theorem}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a0/}
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A. N. Abyzov; I. I. Mukhametgaliev. On Some Matrix Analogs of the Little Fermat Theorem. Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 163-168. http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a0/