Generalized Priestley quasi-orders
type: Item
instance of: scholarly article
title: Generalized Priestley quasi-orders
zbMATH Open document ID: 1243.06003
author: Guram Bezhanishvili
author: Ramon Jansana
published in: Order
publication date: 2011-08-16T00:00:00Z
review text: The authors investigate bounded distributive meet-semilattices, and especially bounded implicative meet-semilattices. First, they develop a new `Priestley-like' duality for the category of bounded distributive meet-semilattices with homomorphisms. Secondly, they extend their description to a duality between the lattice Sub\(_{(0,1)}(S)\) of all subalgebras of a distributive meet-semilattice \(S\) and the space of generalized Priestley quasi-orders GP\((S).\) The final result is a generalization of a characterization given by \textit{M. E. Adams} [Algebra Univers. 3, 216--228 (1973; Zbl 0288.06015)] for bounded distributive lattices. In addition, a similar description of bounded implicative semilattices is obtained, generalizing a former result by \textit{L. L. Esakia} [Sov. Math., Dokl. 15, 147--151 (1974); translation from Dokl. Akad. Nauk SSSR 214, 298--301 (1974; Zbl 0296.02030)] for Heyting algebras.
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06D20
zbMATH DE Number: 5939491
zbMATH Keywords: distributive semilattice
zbMATH Keywords: implicative semilattice
zbMATH Keywords: Heyting algebra
zbMATH Keywords: duality
reviewed by: Tibor Katriňák
MaRDI profile type: Publication
full work available at URL: s11083-010-9166-0
OpenAlex ID: W2105861263
cites work: The Frattini sublattice of a distributive lattice
cites work: Esakia style duality for implicative semilattices
cites work: Priestley style duality for distributive meet-semilattices
cites work: Remarks on Priestley duality for distributive lattices
cites work: Q4049062
cites work: Minimally generated Boolean algebras
cites work: Implicative Semi-Lattices
cites work: Representation of Distributive Lattices by means of ordered Stone Spaces
cites work: Ordered Topological Spaces and the Representation of Distributive Lattices
cites work: Quasiorders and sublattices of distributive lattices
cites work: The Theory of Representation for Boolean Algebras
DOI: 10.1007/S11083-010-9166-0
description: scientific article; zbMATH DE number 5939491