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On the Partition Monoid and Some Related Semigroups


FitzGerald, DG and Lau, KW, On the Partition Monoid and Some Related Semigroups, Bulletin of the Australian Mathematical Society, 83, (2) pp. 273-288. ISSN 0004-9727 (2011) [Refereed Article]


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Copyright © 2011 Cambridge University Press & Australian Mathematical Society

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DOI: doi:10.1017/S0004972710001851


The 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.

Item Details

Item Type:Refereed Article
Keywords:partition monoid, Brauer monoid, ideal structure, natural order.
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Group theory and generalisations
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:FitzGerald, DG (Dr Des FitzGerald)
ID Code:68839
Year Published:2011
Web of Science® Times Cited:22
Deposited By:Mathematics and Physics
Deposited On:2011-03-25
Last Modified:2022-12-19
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