Geodesic
On images of polynomials in finite matrix rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 2, pp. 469-485 
V. V. Kulyamin. On images of polynomials in finite matrix rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 2, pp. 469-485. http://geodesic.mathdoc.fr/item/FPM_1997_3_2_a8/
@article{FPM_1997_3_2_a8,
     author = {V. V. Kulyamin},
     title = {On images of polynomials in finite matrix rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {469--485},
     year = {1997},
     volume = {3},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_2_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the images of polynomials in non-commuting indeterminates in the ring of $2\times2$ matrices over a Galois ring. The main result: a set of $2\times2$ matrices over a Galois ring whose radical has nilpotency index 2, is an image of a polynomial with zero constant term if and only if it contains 0 and is self-conjugate.