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, Volume 30, Issue 1, pp 65–83 | Cite as

Relational Representation of Groupoid Quantales

  • Alessandra Palmigiano
  • Riccardo Re
Open Access
Article

Abstract

In Palmigiano and Re (J Pure Appl Algebra 215(8):1945–1957, 2011), spatial SGF-quantales are axiomatically introduced and proved to be representable as sub unital involutive quantales of quantales arising from set groupoids. In the present paper, spatial SGF-quantales of this class are shown to be optimally representable as unital involutive quantales of relations. The results of the present paper have several aspects in common with Jónsson and Tarski’s representation theory for relation algebras (Jónsson and Tarski, Am J Math 74(2):127–162, 1952).

Keywords

Unital involutive quantale Strongly Gelfand quantale Set groupoid Representation theorem 

Mathematics Subject Classifications (2010)

06D05 06D22 06D50 06F07 18B40 20L05 22A22 54D10 54D30 54D80 

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly

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