2022/09/06 by I. P. Shestakov, Shestakov, I. P., V. S. Bittencourt +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Nonlinear Waves and Solitons #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2209.02770
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.