RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Fundam. Prikl. Mat., 2007, Volume 13, Issue 5, Pages 19–79 (Mi fpm1072)  

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

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.

Full text: PDF file (507 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2009, 156:2, 219–260

Bibliographic databases:

UDC: 512.552.4+512.554.32+512.664.2

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

Citation in format AMSBIB
\Bibitem{Bel07}
\by A.~Ya.~Belov
\paper Burnside-type problems, theorems on height, and independence
\jour Fundam. Prikl. Mat.
\yr 2007
\vol 13
\issue 5
\pages 19--79
\mathnet{http://mi.mathnet.ru/fpm1072}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2379740}
\zmath{https://zbmath.org/?q=an:05633082}
\elib{http://elibrary.ru/item.asp?id=11162684}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 156
\issue 2
\pages 219--260
\crossref{https://doi.org/10.1007/s10958-008-9264-3}
\elib{http://elibrary.ru/item.asp?id=14043109}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-58249100308}


Linking options:
  • http://mi.mathnet.ru/eng/fpm1072
  • http://mi.mathnet.ru/eng/fpm/v13/i5/p19

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Ya. Belov, M. I. Kharitonov, “Subexponential estimates in Shirshov's theorem on height”, Sb. Math., 203:4 (2012), 534–553  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. 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  mathnet  crossref
    3. M. I. Kharitonov, “Two-sided estimates for essential height in Shirshov's Height Theorem”, Moscow University Mathematics Bulletin, 67:2 (2012), 64–68  mathnet  crossref
    4. M. I. Kharitonov, “Piecewise periodicity structure estimates in Shirshov's height theorem”, Moscow University Mathematics Bulletin, 68:1 (2013), 26–31  mathnet  crossref  mathscinet
    5. M. I. Kharitonov, “Otsenki, svyazannye s teoremoi Shirshova o vysote”, Chebyshevskii sb., 15:4 (2014), 55–123  mathnet
  • Фундаментальная и прикладная математика
    Number of views:
    This page:313
    Full text:104
    References:38
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020