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The semigroup generated by the idempotents of a partition monoid
journal contribution
posted on 2023-05-17, 15:43 authored by East, James, Desmond FitzGeraldDesmond FitzGeraldWe 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.
History
Publication title
Journal of AlgebraVolume
372Pagination
108-133ISSN
0021-8693Department/School
School of Natural SciencesPublisher
Academic Press Inc Elsevier SciencePlace of publication
525 B St, Ste 1900, San Diego, USA, Ca, 92101-4495Rights statement
Copyright 2012 Elsevier Inc.Repository Status
- Restricted