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Identities in Vector Spaces Embedded in Finite Associative Algebras

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We study identities in vector spaces embedded in finite associative linear algebras. We prove that the L-variety generated by the space of second order matrices over a finite field possesses finitely many L-subvarieties. We construct examples of a finite two-dimensional vector space, a finite four-dimensional linear algebra, and a ring consisting of 16 elements that have no finite basis of identities.

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References

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Authors and Affiliations

  1. Altai State Pedagogical Academy, 55, Molodezhnaya St., 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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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 15, No. 3, 2015, pp. 69-77.

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Isaev, I.M., Kislitsin, A.V. Identities in Vector Spaces Embedded in Finite Associative Algebras. J Math Sci 221, 849–856 (2017). https://doi.org/10.1007/s10958-017-3273-z

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  • DOI: https://doi.org/10.1007/s10958-017-3273-z

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