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Groupoids on a skew lattice of objects
Citation
FitzGerald, DG, Groupoids on a skew lattice of objects, Art of Discrete and Applied Mathematics, 2, (2) Article 03. ISSN 2590-9770 (2019) [Refereed Article]
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Copyright Statement
Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/
DOI: doi:10.26493/2590-9770.1342.109
Abstract
Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad theorem, we consider a groupoid (small category of isomorphisms) in which the set of objects carries the structure of a skew lattice. The objects act on the morphisms by left and right restriction and extension mappings of the morphisms, imitating those of an inductive groupoid. Conditions are placed on the actions, from which pseudoproducts may be defined. This gives an algebra of signature (2, 2, 1), in which each binary operation has the structure of an orthodox semigroup. In the reverse direction, a groupoid of the kind described may be reconstructed from the algebra.
Item Details
| Item Type: | Refereed Article |
|---|---|
| Keywords: | inductive groupoids, skew lattices, orthodox semigroups |
| 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: | 140437 |
| Year Published: | 2019 |
| Deposited By: | Mathematics |
| Deposited On: | 2020-08-17 |
| Last Modified: | 2020-09-07 |
| Downloads: | 14 View Download Statistics |
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