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Fundamentalnaya i Prikladnaya Matematika, 2007, Volume 13, Issue 5, Pages 19–79
(Mi fpm1072)
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This article is cited in 7 scientific papers (total in 7 papers)
Burnside-type problems, theorems on height, and independence
A. Ya. Belovab a Moscow Institute of Open Education
b Hebrew University of Jerusalem
Abstract:
This review paper is devoted to some questions related to investigations of bases in PI-algebras. The central point is generalization and refinement of the Shirshov height theorem, of the Amitsur–Shestakov hypothesis and of the independence theorem. The paper is mainly inspired by the fact that these topics shed some light on the analogy between structure theory and constructive combinatorial reasoning related to the “microlevel,” to relations in algebras and straightforward calculations. Together with the representation theory of monomial algebras, height and independence theorems are closely connected with combinatorics of words and of normal forms, as well as with properties of primary algebras and with combinatorics of matrix units. Another subject of this paper is an attempt to create a kind of symbolic calculus of operators defined on records of transformations.
Citation:
A. Ya. Belov, “Burnside-type problems, theorems on height, and independence”, Fundam. Prikl. Mat., 13:5 (2007), 19–79; J. Math. Sci., 156:2 (2009), 219–260
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https://www.mathnet.ru/eng/fpm1072 https://www.mathnet.ru/eng/fpm/v13/i5/p19
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Abstract page: | 430 | Full-text PDF : | 145 | References: | 55 | First page: | 1 |
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