This article is cited in 5 scientific papers (total in 5 papers)
Burnside-type problems, theorems on height, and independence
A. Ya. Belovab
a Moscow Institute of Open Education
b Hebrew University of Jerusalem
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.
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Journal of Mathematical Sciences (New York), 2009, 156:2, 219–260
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
Citation in format AMSBIB
\paper Burnside-type problems, theorems on height, and independence
\jour Fundam. Prikl. Mat.
\jour J. Math. Sci.
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This publication is cited in the following articles:
A. Ya. Belov, M. I. Kharitonov, “Subexponential estimates in Shirshov's theorem on height”, Sb. Math., 203:4 (2012), 534–553
A. Ya. Belov, M. I. Kharitonov, “Subexponential estimates in the height theorem and estimates on numbers of periodic parts of small periods”, J. Math. Sci., 193:4 (2013), 493–515
M. I. Kharitonov, “Two-sided estimates for essential height in Shirshov's Height Theorem”, Moscow University Mathematics Bulletin, 67:2 (2012), 64–68
M. I. Kharitonov, “Piecewise periodicity structure estimates in Shirshov's height theorem”, Moscow University Mathematics Bulletin, 68:1 (2013), 26–31
M. I. Kharitonov, “Otsenki, svyazannye s teoremoi Shirshova o vysote”, Chebyshevskii sb., 15:4 (2014), 55–123
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