FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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

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The main result of this article is the following: a subset $A$ of $2$´ 2 matrices over the ring $$Z/8Z is the range of a polynomial in noncommuting indeterminates with coefficients in $$Z/8Z and without constant term if and only if $A$ contains $0$ and is selfsimilar, that is $$a A a ^-1 Í A for each invertible $2$´ 2 matrix $$a.

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Last modified: April 11, 2000