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Sbornik: Mathematics, 2015, Volume 206, Issue 10, Pages 1440–1462
DOI: https://doi.org/10.1070/SM2015v206n10ABEH004501 (Mi sm8454) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Exponential growth of codimensions of identities of algebras with unity

M. V. Zaiceva, D. Repovšb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b University of Ljubljana, Slovenia
English version PDF (552 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/SM2015v206n10ABEH004501
Abstract: The asymptotic behaviour is studied of exponentially bounded sequences of codimensions of identities of algebras with unity. A series of algebras is constructed for which the base of the exponential increases by exactly 1 when an outer unity is adjoined to the original algebra. It is shown that the PI-exponents of unital algebras can take any value greater than 2, and the exponents of finite-dimensional unital algebras form a dense subset in the domain $[2,\infty)$.
Bibliography: 34 titles.
Keywords: identities, codimensions, exponential growth.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00234a
Slovenian Research Agency P1-0292-0101
J1-5435-0101
J1-6721-0101
This research was supported by the Russian Foundation for Basic Research (grant no. 13-01-00234a) and the Slovenian Research Agency (grant nos. P1-0292-0101, J1-5435-0101, and J1-6721-0101).
Received: 01.12.2014 and 13.04.2015
Bibliographic databases:
Document Type: Article
UDC: 512.572
MSC: Primary 17A30; Secondary 16R10
Language: English
Original paper language: Russian
Citation: M. V. Zaicev, D. Repovš, “Exponential growth of codimensions of identities of algebras with unity”, Sb. Math., 206:10 (2015), 1440–1462
Citation in format AMSBIB
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\paper Exponential growth of codimensions of identities of algebras with unity
\jour Sb. Math.
\yr 2015
\vol 206
\issue 10
\pages 1440--1462
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  • https://doi.org/10.1070/SM2015v206n10ABEH004501
  • https://www.mathnet.ru/eng/sm/v206/i10/p103
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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