The semigroup generated by the idempotents of a partition monoid
journal contribution
posted on 2023-05-17, 15:43authored byEast, James, Desmond FitzGerald
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.
History
Publication title
Journal of Algebra
Volume
372
Pagination
108-133
ISSN
0021-8693
Department/School
School of Natural Sciences
Publisher
Academic Press Inc Elsevier Science
Place of publication
525 B St, Ste 1900, San Diego, USA, Ca, 92101-4495