Some notes on the ternary modular commutator

TL;DR

This paper introduces a relation for the ternary commutator in congruence modular varieties and explores its properties to advance the understanding of higher commutators in this algebraic context.

Contribution

It defines a new relation characterizing the ternary commutator and uses it to deepen the theoretical framework of higher commutators in congruence modular varieties.

Findings

Established properties of the ternary commutator relation

Enhanced understanding of higher commutator theory

Provided tools for future algebraic investigations

Abstract

We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.