Steady growth of length function and Malcev algebras

TL;DR

This paper studies algebras with linearly bounded length, demonstrating that Malcev algebras are included in this class and determining the precise maximum length for them.

Contribution

It introduces the class of steadily growing length algebras and establishes the exact upper bound for the length of Malcev algebras.

Findings

Malcev algebras belong to the class of steadily growing length algebras

The exact upper bound for the length of Malcev algebras is determined

The concept of linear growth of algebra length is formalized

Abstract

We introduce and investigate the algebras of steadily growing length, that is the class of algebras, where the length is bounded by a linear function of the dimension. In particular we show that Malcev algebras belong to this class and establish the exact upper bound for its length.