FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

V. V. Kuliamin

Abstract

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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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Last modified: April 11, 2000