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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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/

[1] W. K. Nicholson, “Lifting idempotents and exchange rings”, Trans. Amer. Math. Soc., 229 (1977), 269–278 | DOI | MR | Zbl

[2] A. J. Diesl, “Nil clean rings”, J. Algebra, 383 (2013), 197–211 | DOI | MR | Zbl

[3] S. Breaz, G. Călugăreanu, P. Danchev, T. Micu, “Nil-clean matrix rings”, Linear Algebra Appl., 439:10 (2013), 3115–3119 | DOI | MR | Zbl

[4] V. I. Arnold, “Dinamika Ferma, arifmetika matrits, konechnaya okruzhnost i konechnaya ploskost Lobachevskogo”, Funkts. analiz i ego pril., 38:1 (2004), 1–15 | DOI | MR | Zbl

[5] D. S. Passman, The Algebraic Structure of Group Rings, Robert E. Krieger Publ., Melbourne, FL, 1985 | MR | Zbl

[6] K. R. Goodearl, Von Neumann Regular Rings, Monogr. Stud. in Math., 4, Pitman, Boston, MA, 1979 | MR | Zbl

[7] K. C. O'Meara, J. Clark, C. I. Vinsonhaler, Advanced Topics in Linear Algebra. Weaving Matrix Problems Through the Weyr Form, Oxford Univ. Press, Oxford, 2011 | MR | Zbl