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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: | 3 |
| Deposited By: | Mathematics |
| Deposited On: | 2022-02-05 |
| Last Modified: | 2022-03-15 |
| Downloads: | 0 |
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