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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






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


Algebra Logika, 2011, Volume 50, Number 5, Pages 563–594 (Mi al503)  

This article is cited in 7 scientific papers (total in 7 papers)

Identities of unitary finite-dimensional algebras

M. V. Zaitsev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia

Abstract: We deal with growth functions of sequences of codimensions of identities in finite-dimensional algebras with unity over a field of characteristic zero. For three-dimensional algebras, it is proved that the codimension sequence grows asymptotically as $a^n$, where $a$ is $1,2$, or $3$. For arbitrary finite-dimensional algebras, it is shown that the codimension growth either is polynomial or is not slower than $2^n$. We give an example of a finite-dimensional algebra with growth rate $a^n$ with fractional exponent $a=\frac3{\sqrt[3]4}+1$.

Keywords: finite-dimensional unitary algebra, growth function of sequences of codimensions of identities.

Full text: PDF file (298 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2011, 50:5, 381–404

Bibliographic databases:

UDC: 512.57
Received: 03.12.2010
Revised: 08.04.2011

Citation: M. V. Zaitsev, “Identities of unitary finite-dimensional algebras”, Algebra Logika, 50:5 (2011), 563–594; Algebra and Logic, 50:5 (2011), 381–404

Citation in format AMSBIB
\Bibitem{Zai11}
\by M.~V.~Zaitsev
\paper Identities of unitary finite-dimensional algebras
\jour Algebra Logika
\yr 2011
\vol 50
\issue 5
\pages 563--594
\mathnet{http://mi.mathnet.ru/al503}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2907408}
\zmath{https://zbmath.org/?q=an:06115013}
\transl
\jour Algebra and Logic
\yr 2011
\vol 50
\issue 5
\pages 381--404
\crossref{https://doi.org/10.1007/s10469-011-9151-8}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000297813600001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-82955163226}


Linking options:
  • http://mi.mathnet.ru/eng/al503
  • http://mi.mathnet.ru/eng/al/v50/i5/p563

    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. O. E. Bezushchak, A. A. Beljaev, M. V. Zaicev, “Codimension growth of algebras with adjoint unit”, J. Math. Sci., 206:5 (2015), 462–473  mathnet  crossref  mathscinet
    2. S. P. Mishchenko, O. A. Bogdanchuk, “PI-exponents of some simple algebras with unit”, J. Math. Sci., 206:6 (2015), 688–693  mathnet  crossref  mathscinet
    3. M. V. Zaicev, D. Repovš, “A Four-Dimensional Simple Algebra with Fractional PI-Exponent”, Math. Notes, 95:4 (2014), 487–499  mathnet  crossref  crossref  mathscinet  isi  elib
    4. M. V. Zaicev, D. Repovš, “Exponential growth of codimensions of identities of algebras with unity”, Sb. Math., 206:10 (2015), 1440–1462  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Repovs D., Zaicev M., “Numerical Invariants of Identities of Unital Algebras”, Commun. Algebr., 43:9 (2015), 3823–3839  crossref  mathscinet  zmath  isi  elib  scopus
    6. M. V. Zaicev, “Growth of codimensions of metabelian algebras”, Moscow University Mathematics Bulletin, 72:6 (2017), 233–237  mathnet  crossref  mathscinet  isi
    7. Repovs D.D., Zaicev M.V., “Z(2)-Graded Codimensions of Unital Algebras”, Int. J. Algebr. Comput., 28:3 (2018), 483–500  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
    Number of views:
    This page:268
    Full text:71
    References:36
    First page:7

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019