I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2007, VOLUME 13, NUMBER 2, PAGES 3-29
A. Ya. Belov
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The paper is devoted to relations between the Kurosh problem and the
Shirshov height theorem.
The central point and main technical tool is the identity of
The main result of this paper is the following.
The paper also contains a new proof of the Razmyslov--Kemer--Braun theorem on radical nilpotence of affine PI-algebras. This proof allows one to obtain some constructive estimates.
The main goal of the paper is to develope a "virtual operator calculus." Virtual operators (pasting, deleting and transfer) depend not only on an element of the algebra but also on its representation.
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Last modified: May 23, 2007