A new properties of varieties of Leibnitz algebras

TL;DR

This paper explores new properties of varieties of Leibnitz algebras over fields of zero characteristic, providing conditions for finiteness and defining bases of identities for specific varieties.

Contribution

It introduces a sufficient condition for the finiteness of colength in Leibnitz algebra varieties and establishes bases of identities for a particular variety V3.

Findings

Proved a sufficient condition for finiteness colength.

Defined the basis of identities for variety V3.

Established the basis of multilinear identities.

Abstract

The paper is devoted to two new results concerning varieties of Leibnitz algebras over a field of the zero characteristic. Here is proved the sufficient condition for finiteness colength of variety of Leibnitz algebras. Here is also defined the basis of identities of variety V3 of Leibnitz algebras and the basis of its multilinear part.