RUS  ENG
Full version
JOURNALS // Algebra i logika // Archive

Algebra Logika, 2023 Volume 62, Number 6, Pages 786–808 (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

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.

UDC: 512.554:512.554.5:512.554.7:512.552

Received: 11.09.2022
Revised: 02.12.2024

DOI: 10.33048/alglog.2023.62.605



© Steklov Math. Inst. of RAS, 2025