East, James and FitzGerald, DG, The semigroup generated by the idempotents of a partition monoid, Journal of Algebra, 372 pp. 108-133. ISSN 0021-8693 (2012) [Refereed Article]
Copyright 2012 Elsevier Inc.
We study the idempotent generated subsemigroup of the partition monoid. In the finite case this subsemigroup consists of the identity and all the singular partitions. In the infinite case, the subsemigroup is described in terms of certain parameters that measure how far a partition is from being a permutation. As one of several corollaries, we deduce Howieʼs description from 1966 of the semigroup generated by the idempotents of a full transformation semigroup.
|Item Type:||Refereed Article|
|Keywords:||partition monoids, transformation semigroups, symmetric inverse semigroups, dual symmetric inverse semigroups, idempotents|
|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|
|Author:||FitzGerald, DG (Dr Des FitzGerald)|
|Web of Science® Times Cited:||16|
|Deposited By:||Mathematics and Physics|
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