Journal of Mathematical Sciences

, Volume 156, Issue 2, pp 219–260 | Cite as

Burnside-type problems, theorems on height, and independence

  • A. Ya. BelovEmail author


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 aim of this paper is an attempt to create a kind of symbolic calculus of operators defined on records of transformations.


Hilbert Series Minimal Dimension Minimal Image Monomial Algebra Kirillov Dimension 
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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Moscow Institute of Open EducationMoscowRussia
  2. 2.International University of BremenBremenRussia
  3. 3.Hebrew University of JerusalemJerusalemIsrael

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