Nonmatrix varieties of nonassociative algebras

TL;DR

This paper extends the concept of nonmatrix varieties from associative to nonassociative algebras, providing generalized characterizations for alternative, Jordan, and other algebra varieties, advancing understanding in algebraic structure classification.

Contribution

It introduces the notion of nonmatrix varieties for nonassociative algebras and generalizes existing characterizations to broader algebraic classes.

Findings

Extended nonmatrix variety concept to nonassociative algebras

Generalized characterizations for alternative and Jordan varieties

Enhanced classification framework for algebraic varieties

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.