Varieties of associative algebras with an identity of third degree

TL;DR

This paper classifies all varieties of associative algebras over characteristic zero fields that satisfy a specific polynomial identity of third degree, providing a comprehensive structural understanding.

Contribution

It offers a complete description of associative algebra varieties satisfying a third-degree polynomial identity, filling a gap in algebraic classification.

Findings

Classification of all such algebra varieties

Structural characterization of these varieties

Complete description of identities of third degree

Abstract

We give a complete description of the varieties of associative algebras over a field of characteristic zero which satisfy a polynomial identity of third degree.