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 Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 328–343 (Mi semr590)

Mathematical logic, algebra and number theory

The Identities of vector spaces embedded in a linear algebra

I. M. Isaev, A. V. Kislitsin

Altai State Pedagogical University

Abstract: In this paper we study the identities of vector spaces embedded in linear algebras. We prove that the identities of the class of all vector spaces embedded in associative algebras do not follow from a finite set of the identities that are true in this class. Similar result is proved for the spaces embedded in Lie algebras. We constructed the example of a four-dimensional algebra over a field of characteristic zero which is a strongly not finitely based. The authors describe strongly nonfinitely based vector spaces that are finite-dimensional associative algebras with unity over a field of characteristic zero.

Keywords: Multiplicative vector pair, identity of pair, $L$-variety, linear algebra, associative algebras, Lie algebras, inherently nonfinitely based algebra, strongly nonfinitely based algebra.

DOI: https://doi.org/10.17377/semi.2015.12.027

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UDC: 512.552.4, 512.554.1
MSC: 16R10, 17A30
Received November 19, 2014, published May 27, 2015

Citation: I. M. Isaev, A. V. Kislitsin, “The Identities of vector spaces embedded in a linear algebra”, Sib. Èlektron. Mat. Izv., 12 (2015), 328–343

Citation in format AMSBIB
\Bibitem{IsaKis15} \by I.~M.~Isaev, A.~V.~Kislitsin \paper The Identities of vector spaces embedded in a linear algebra \jour Sib. \Elektron. Mat. Izv. \yr 2015 \vol 12 \pages 328--343 \mathnet{http://mi.mathnet.ru/semr590} \crossref{https://doi.org/10.17377/semi.2015.12.027} `

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This publication is cited in the following articles:
1. A. V. Kislitsin, “The Specht property of $L$-varieties of vector spaces”, Algebra and Logic, 56:5 (2017), 362–369
2. A. V. Kislitsin, “Simple finite-dimensional algebras without finite basis of identities”, Siberian Math. J., 58:3 (2017), 461–466
3. A. V. Kislitsin, “On nonnilpotent almost commutative $L$-varieties of vector spaces”, Siberian Math. J., 59:3 (2018), 458–462
4. A. V. Kislitsin, “The Specht property of $L$-varieties of vector spaces over an arbitrary field”, Algebra and Logic, 57:5 (2018), 360–367
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