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arXiv · 2209.02770

Nonmatrix varieties of nonassociative algebras

I. P. Shestakov·V. S. Bittencourt
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Abstract

A variety of associative algebras is called nonmatrix if it does not contain the algebra of 2 x 2 matrices over the given field. Nonmatrix varieties were introduced and studied by V.N.Latyshev in relation with the Specht problem. Some characterizations of nonmatrix varieties were obtained in the paper [10]. In the given paper the notion of nonmatrix variety is extended for nonassociative algebras, and the characterization from [10] is generalized for alternative, Jordan, and some other varieties of algebras.

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I. P. Shestakov, V. S. Bittencourt. 2022-09-06. Nonmatrix varieties of nonassociative algebras. https://arxiv.org/abs/2209.02770

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