John Fountain (University of York)

Thursday 6th September, 12.05-12.55pm, Carslaw 373 (***NOTE UNUSUAL DAY***)

Unique factorisation in noncommutative monoids

We consider right cancellative monoids C in which every nonunit can be written as a product of atoms (irreducible elements) with such factorisations satisfying a uniqueness property, and with C having the property that for any element c, the partially ordered set of principal left ideals containing Cc is a distributive lattice. We call such a monoid a unique factorisation monoid (UFM). Examples of UFMs include commutative unique factorisation monoids, free monoids and graph monoids (right-angled Artin monoids). Generalising results of Mark Lawson, it can be shown that a UFM is a Zappa-Szép product of a group and a graph monoid.

We also make some remarks about the inverse hulls of these monoids.