(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 2, PAGES 469-485

## On images of polynomials in finite matrix rings

V. V. Kulyamin

Abstract

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 We study the images of polynomials in non-commuting indeterminates in the ring of $2\times 2$ matrices over a Galois ring. The main result: a set of $2\times 2$ 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. 

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