On the partition Monoid.pdf (190.87 kB)
On the Partition Monoid and Some Related Semigroups
journal contribution
posted on 2023-05-17, 05:32 authored by Desmond FitzGeraldDesmond FitzGerald, Lau, KWThe partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new interpretation of the natural order on the transformation semigroup. The results are also used to describe the ideal lattices of the straight and twisted partition monoids and the Brauer monoid.
History
Publication title
Bulletin of the Australian Mathematical SocietyVolume
83Pagination
273-288ISSN
0004-9727Department/School
School of Natural SciencesPublisher
Australian Mathematics Publishing Association IncPlace of publication
United KingdomRights statement
Copyright © 2011 Cambridge University Press & Australian Mathematical SocietyRepository Status
- Open