Geodesic
On ranges of polynomials in the~ring $M_2(\mathbb Z/8\mathbb Z)$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 275-280.

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The main result of this article is the following: a subset $A$ of $2\times2$ matrices over the ring $\mathbb Z/8\mathbb Z$ is the range of a polynomial in noncommuting indeterminates with coefficients in $\mathbb Z/8\mathbb Z$ and without constant term if and only if $A$ contains 0 and is selfsimilar, that is $\alpha A\alpha^{-1}\subseteq A$ for each invertible $2\times2$ matrix $\alpha$. 
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     author = {V. V. Kulyamin},
     title = {On ranges of polynomials in the~ring $M_2(\mathbb Z/8\mathbb Z)$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {275--280},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a21/}
}
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V. V. Kulyamin. On ranges of polynomials in the~ring $M_2(\mathbb Z/8\mathbb Z)$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 275-280. http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a21/