FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 8, PAGES 159-168

Automorphisms and model-theory questions for nilpotent matrix groups and rings

V. M. Levchuk
E. V. Minakova

Abstract

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Let $R\text{'}\; =\; NT(m,S)$. The purpose of the paper is the investigation of elementary equivalences $UT(n,K)$º UT(m,S) and $$L (R) º L (R') for arbitrary associative coefficient rings with identity. The main theorem gives the description of such equivalences for $n\; >\; 4$. In addition, we investigate isomorphisms and elementary equivalence of Jordan niltriangular matrix rings.

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