Semilattice-based dualities
type: Item
instance of: scholarly article
title: Semilattice-based dualities
zbMATH Open document ID: 0854.08007
DOI: 10.1007/BF00370148
author: J. D. H. Smith
author: Anna Romanowska
published in: Studia Logica
publication date: 1997-01-19T00:00:00Z
review text: The authors consider a duality between a variety of universal algebras and a category of what they call ``representation spaces'', such as the Stone duality for the Boolean algebras, etc. They extend their duality to various ``regularizations'' of a given variety using the Płonka sum construction which is also expressed in the language of sheaves and étale spaces. Various examples of regularizations of the Priestley, Stone and Pontryagin dualities are described. In particular the duality for the distributive bisemilattices without constants, deduced [\textit{G. Gierz} and \textit{A. B. Romanowska}, J. Aust. Math. Soc., Ser. A 51, 247-275 (1991; Zbl 0751.06008)] from the Priestley duality for distributive lattices, is obtained as a special case.
reviewed by: George Janelidze
Mathematics Subject Classification ID: 08C05
zbMATH DE Number: 883891
zbMATH Keywords: Priestley duality
zbMATH Keywords: Pontryagin duality
zbMATH Keywords: regular identities
zbMATH Keywords: category of representation spaces
zbMATH Keywords: variety of universal algebras
zbMATH Keywords: Stone duality
zbMATH Keywords: Płonka sum
zbMATH Keywords: sheaves
zbMATH Keywords: étale spaces
zbMATH Keywords: regularizations
zbMATH Keywords: distributive bisemilattices
MaRDI profile type: Publication
cites work: Q5532570
cites work: Q5772179
cites work: Q3969000
cites work: Q3988091
cites work: The l 1 -Algebra of a Commutative Semigroup
cites work: The Pontryagin duality of compact O-dimensional semilattices and its applications
cites work: Q4126563
cites work: Q3987716
cites work: Q3965241
cites work: Q5639839
cites work: Sheaves in geometry and logic: a first introduction to topos theory
cites work: On distributive quad-lattices
cites work: On a method of construction of abstract algebras
cites work: On equational classes of abstract algebras defined by regular equations
cites work: On the sum of a direct system of universal algebras with nullary polynomials
cites work: Q3041261
cites work: Q3979109
cites work: Q4029633
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: On regular and regularized varieties
cites work: Q3698853
cites work: Subalgebra systems of idempotent entropic algebras
cites work: On the structure of semilattice sums
cites work: Duality for semilattice representations
cites work: Q3866256
description: scientific article; zbMATH DE number 883891