The Commutator as Least Fixed Point of a Closure Operator

TL;DR

This paper introduces a new approach to computing the non-modular commutator using a closure operator, simplifying the process inspired by Kearnes' work.

Contribution

It offers a novel description of the non-modular commutator based on a closure operator, providing a straightforward computational method.

Findings

Provides a simple recipe for computing the commutator

Extends understanding of non-modular commutator properties

Builds on Kearnes' framework for algebraic structures

Abstract

We present a description of the (non-modular) commutator, inspired by that of Kearnes in~\cite[p.~930]{MR1358491}, that provides a simple recipe for computing the commutator.