Geodesic
Nonmatrix varieties of nonassociative algebras
Algebra i logika, Tome 62 (2023) no. 6, pp. 786-808

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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. 
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     author = {I. P. Shestakov and V. S. Bittencourt},
     title = {Nonmatrix varieties of nonassociative algebras},
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I. P. Shestakov; V. S. Bittencourt. Nonmatrix varieties of nonassociative algebras. Algebra i logika, Tome 62 (2023) no. 6, pp. 786-808. http://geodesic.mathdoc.fr/item/AL_2023_62_6_a4/