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On the partition monoid and some related semigroups

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FitzGerald, DG and Lau, KW (2010) On the partition monoid and some related semigroups. Bulletin of the Australian Mathematical Society (Publis). ISSN 0004-9727 (In Press)

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Abstract

The partition monoid is a salient natural example of a *-regular semi- group. We find a Galois connexion 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 char- acterise the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterisation 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.

Item Type: Article
Keywords: partition monoid, Brauer monoid, ideal structure, natural order
Journal or Publication Title: Bulletin of the Australian Mathematical Society
ISSN: 0004-9727
Identification Number - DOI: 10.1017/S0004972710001851
Additional Information: Earlier version - FitzGerald, DG and Lau, KW (2005) Green's relations on the partition monoid and several related monoids. In: Special Interest Meeting on Semigroups and Related Mathematics, 27-28 June 2005, Sydney, Austalia. - This is a corrected and substantially enlarged version, with a new title. Submitted to Bulletin of the Australian Mathematical Society 17-06-10.
Date Deposited: 20 Oct 2010 05:44
Last Modified: 18 Nov 2014 04:12
URI: http://eprints.utas.edu.au/id/eprint/10039
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