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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 anthonyh@maths.usyd.edu.au. |