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Algebra i logika, 2023, Volume 62, Number 6, Pages 786–808
DOI: https://doi.org/10.33048/alglog.2023.62.605 (Mi al2788) 		 
Nonmatrix varieties of nonassociative algebras

I. P. Shestakovab, V. S. Bittencourtc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Federal University of São Paulo
c Universidade Federal do Oeste da Bahia
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DOI: https://doi.org/10.33048/alglog.2023.62.605
Abstract: A variety of associative algebras is nonmatrix if it does not contain the algebra of $2\times 2$ matrices over a given field. Nonmatrix varieties were introduced and studied by V. N. Latyshev in [Algebra and Logic, 16, No. 2, 98—122 (1977); Algebra and Logic, 16, No. 2, 122—133 (1977); Mat. Zam., 27, No. 1, 147—156 (1980)] in connection with the Specht problem. A series of equivalent characterizations of nonmatrix varieties was obtained in [Isr. J. Math., 181, No. 1, 337—348 (2011)]. In the present paper, the notion of nonmatrix variety is extended to nonassociative algebras, and their characterization from the last-mentioned paper is generalized to alternative, Jordan, and some other varieties of algebras.
Keywords: nonmatrix variety, alternative algebra, Jordan algebra, noncommutative Jordan algebra.
Funding agency Grant number
National Council for Scientific and Technological Development (CNPq) 304313/2019-0
Fundação de Amparo à Pesquisa do Estado de São Paulo 2018/23690-6
Supported by FAPESP (project No. 2018/23690-6) and by CNPq (project No. 304313/2019-0).
Received: 11.09.2022
Revised: 02.12.2024
English version:
Algebra and Logic, 2024, Volume 62, Issue 6, Pages 532–547
DOI: https://doi.org/10.1007/s10469-024-09763-0
Document Type: Article
UDC: 512.554:512.554.5:512.554.7:512.552
Language: Russian
Citation: I. P. Shestakov, V. S. Bittencourt, “Nonmatrix varieties of nonassociative algebras”, Algebra Logika, 62:6 (2023), 786–808; Algebra and Logic, 62:6 (2024), 532–547
Citation in format AMSBIB
\Bibitem{SheBit23}
\by I.~P.~Shestakov, V.~S.~Bittencourt
\paper Nonmatrix varieties of nonassociative algebras
\jour Algebra Logika
\yr 2023
\vol 62
\issue 6
\pages 786--808
\mathnet{http://mi.mathnet.ru/al2788}
\transl
\jour Algebra and Logic
\yr 2024
\vol 62
\issue 6
\pages 532--547
\crossref{https://doi.org/10.1007/s10469-024-09763-0}
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