Nilpotence dans les alg\`ebres de Malcev

TL;DR

This paper proves that right nilpotent Malcev algebras are also strongly nilpotent, establishing an explicit upper bound on the degree of strong nilpotency based on the degree of right nilpotency.

Contribution

It provides a new upper bound linking right nilpotency and strong nilpotency in Malcev algebras, enhancing understanding of their structural properties.

Findings

Right nilpotent Malcev algebras are strongly nilpotent.

The degree of strong nilpotency is at most 4n^2 - 2n + 1 for degree n right nilpotency.

Establishes a quantitative relationship between different types of nilpotency.

Abstract

The main result is to prove that if a Malcev algebra $A$ is \textit{right nilpotent} of degree $n$, then $A$ is \textit{strongly nilpotent} of degree less or equals to $4n^2-2n+1$.