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Identities in vector spaces and examples of finite-dimensional linear algebras having no finite basis of identities

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Algebra and Logic Aims and scope

Identities in vector spaces embedded in linear algebras are considered. Issues in finite basicity of identities for vector spaces, as well as for finite-dimensional linear (nonassociative) algebras, are investigated. Essentially infinitely based and strongly infinitely based vector spaces and nonassociative linear algebras are exemplified.

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Authors and Affiliations

  1. Altai State Pedagogical Academy, ul. Molodezhnaya 55, Barnaul, 656031, Russia

    I. M. Isaev & A. V. Kislitsin

Authors
  1. I. M. Isaev
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  2. A. V. Kislitsin
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Correspondence to I. M. Isaev.

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*Supported by RFBR (project No. 12.01.00329a) and by the Russian Ministry of Education and Science through gov. contract for 2012-2014 (project No. 1.4311.2011).

Translated from Algebra i Logika, Vol. 52, No. 4, pp. 435-460, July-August, 2013.

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Isaev, I.M., Kislitsin, A.V. Identities in vector spaces and examples of finite-dimensional linear algebras having no finite basis of identities. Algebra Logic 52, 290–307 (2013). https://doi.org/10.1007/s10469-013-9243-8

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  • DOI: https://doi.org/10.1007/s10469-013-9243-8

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