A cancellativity criterion for presented monoids

TL;DR

This paper introduces a new, general criterion for cancellativity in presented monoids using factor reversing, applicable regardless of the number of relations, with applications to colored braid monoids.

Contribution

It extends existing cancellativity criteria by removing restrictions on the number of relations, using a novel factor reversing technique.

Findings

Established a new cancellativity criterion for monoids

Applied the criterion to colored extensions of Artin's braid monoid

Demonstrated the criterion's generality and effectiveness

Abstract

We establish a new, fairly general cancellativity criterion for a presented monoid that properly extends the previously known related criteria. It is based on a new version of the word transformation called factor reversing, and its specificity is to avoid any restriction on the number of relations in the presentation. As an application, we deduce the cancellativity of some natural extension of Artin's braid monoid in which crossings are colored.