(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 275-280

## On ranges of polynomials in the ring $M$2(Z/8Z)

V. V. Kuliamin

Abstract

View as HTML     View as gif image    View as LaTeX source

 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 $\alpha$. 

All articles are published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k00/k001/k00122t.htm