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Trace- and pseudo-products: restriction-like semigroups with a band of projections

Citation

FitzGerald, DG and Kinyon, MK, Trace- and pseudo-products: restriction-like semigroups with a band of projections, Semigroup Forum, 103, (3) pp. 848-866. ISSN 0037-1912 (2021) [Refereed Article]

Copyright Statement

The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021

DOI: doi:10.1007/s00233-021-10221-x

Abstract

We 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.

Item Details

Item Type:Refereed Article
Keywords:ESN theorem, Ehresmann semigroup, restriction semigroup
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:148746
Year Published:2021
Web of Science® Times Cited:2
Deposited By:Mathematics
Deposited On:2022-02-05
Last Modified:2022-03-15
Downloads:0

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