On the partition monoid and some related semigroups
FitzGerald, DG and Lau, KW (2010) On the partition monoid and some related semigroups. Bulletin of the Australian Mathematical Society (Published online: 6 Dec 2010). ISSN 0004-9727 (In Press)
This is the latest version of this item.
Official URL: http://dx.doi.org/10.1017/S0004972710001851
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.
|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.|
|Keywords:||partition monoid, Brauer monoid, ideal structure, natural
|Deposited By:||Dr D. G. FitzGerald|
|Deposited On:||20 Oct 2010 16:44|
|Last Modified:||31 Jan 2011 15:53|
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