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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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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
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