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Trace- and pseudo-products: restriction-like semigroups with a band of projections
journal contribution
posted on 2023-05-21, 05:37 authored by Desmond FitzGeraldDesmond FitzGerald, Kinyon, MKWe ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem and its generalisation to ample semigroups. Unlike some other variants of ESN, it is self-dual (two-sided), and the condition of commuting projections is relaxed. The condition that projections form a band (are closed under multiplication) is shown to be a very natural one. One-sided reducts are considered, and compared to (generalised) D-semigroups. Finally the special case when the category is a groupoid is examined.
History
Publication title
Semigroup ForumVolume
103Pagination
848-866ISSN
0037-1912Department/School
School of Natural SciencesPublisher
Springer-VerlagPlace of publication
175 Fifth Ave, New York, USA, Ny, 10010Rights statement
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021Repository Status
- Restricted