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Algebra Logika, 2015, Volume 54, Number 3, Pages 315–325 (Mi al696)  

This article is cited in 1 scientific paper (total in 1 paper)

An example of a central simple commutative finite-dimensional algebra with an infinite basis of identities

A. V. Kislitsin

Altai State Pedagogical University, ul. Molodezhnaya 55, Barnaul, 656031, Russia

Abstract: In 1993 I. P. Shestakov came up with the question whether there exists a central simple finite-dimensional algebra over a field of characteristic 0, whose identities are not given by a finite set (Dniester Notebook, Question 3.103). In 2012 I. M. Isaev and the author constructed a desired example, giving an affirmative answer to the question posed. Here research into Shestakov's question is continued for the case of commutative algebras. A seven-dimensional central simple commutative algebra over a field of characteristics 0 having no finite basis of identities is exemplified.

Keywords: simple algebra, identity of algebra, basis of identities, infinitely based algebra.

DOI: https://doi.org/10.17377/alglog.2015.54.302

Full text: PDF file (154 kB)
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English version:
Algebra and Logic, 2015, 54:3, 204–210

Bibliographic databases:

UDC: 512.554.1
Received: 20.11.2014

Citation: A. V. Kislitsin, “An example of a central simple commutative finite-dimensional algebra with an infinite basis of identities”, Algebra Logika, 54:3 (2015), 315–325; Algebra and Logic, 54:3 (2015), 204–210

Citation in format AMSBIB
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\by A.~V.~Kislitsin
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\crossref{https://doi.org/10.17377/alglog.2015.54.302}
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\jour Algebra and Logic
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\issue 3
\pages 204--210
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    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. V. Kislitsin, “Simple finite-dimensional algebras without finite basis of identities”, Siberian Math. J., 58:3 (2017), 461–466  mathnet  crossref  crossref  isi  elib  elib
  • Алгебра и логика Algebra and Logic
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