SMS scnews item created by Anthony Henderson at Tue 28 Aug 2007 1227
Type: Seminar
Distribution: World
Expiry: 6 Sep 2007
Calendar1: 6 Sep 2007 1205-1255
CalLoc1: Carslaw 373
CalTitle1: Algebra Seminar: Fountain -- Unique factorisation in noncommutative monoids

Algebra Seminar

Unique factorisation in noncommutative monoids

John Fountain

***NOTE UNUSUAL DAY*** 6th September, 12:05-12:55pm, Carslaw 373


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.

After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

Anthony Henderson

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