A CANCELLATIVITY CRITERION FOR PRESENTED MONOIDS

Patrick Dehornoy (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We establish a new, fairly general cancellativity criterion for a presented monoid that properly extends the previously known 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.

Mots clés: Artin–Tits group; Semigroup presentation; Van Kampen diagram; Rewrite system; Cancellativity; Word problem; Garside monoid; Group of fractions; Monoid embeddability

Domaines: Théorie des groupes [math.GR]

Patrick Dehornoy. A CANCELLATIVITY CRITERION FOR PRESENTED MONOIDS. 2018. ⟨hal-01705730v1⟩