Boolean products of lattices
type: Item
instance of: scholarly article
title: Boolean products of lattices
zbMATH Open document ID: 0869.06005
DOI: 10.1007/BF00389840
author: Gary D. Crown
author: John Harding
author: Melvin F. Janowitz
published in: Order
publication date: 1997-08-25T00:00:00Z
review text: The authors focus on the Pierce sheaf representation of bounded lattices and give a detailed account of conditions on a bounded lattice \(L\). Further, they present a sequence of technical lemmas which provide the basic link between properties of the Pierce sheaf of a lattice and lattice-theoretic properties of its centre. In the following sections, they characterize Hausdorff lattices, the connection between weakly Hausdorff lattices and Hausdorff lattices. They study Hausdorff lattices which have the extended patchwork property. Finally, they give examples which illustrate their results.
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 06E15
zbMATH DE Number: 947533
zbMATH Keywords: Boolean products
zbMATH Keywords: Stone space
zbMATH Keywords: Pierce sheaf representation
zbMATH Keywords: bounded lattices
zbMATH Keywords: centre
zbMATH Keywords: Hausdorff lattices
zbMATH Keywords: weakly Hausdorff lattices
zbMATH Keywords: extended patchwork property
MaRDI profile type: Publication
cites work: Q4083730
cites work: Hüllensysteme und Erweiterung von Quasi‐Ordnungen
cites work: Subdirect unions in universal algebra
cites work: Pierce sheaves of non-commutative rings
cites work: Q3934450
cites work: Sheaf Constructions and Their Elementary Properties
cites work: Q3996162
cites work: Representation of Łukasiewicz and Post algebras by continuous functions
cites work: The lattice of global sections of sheaves of chains over Boolean spaces
cites work: Representations by algebras of sections over Boolean spaces
cites work: Q4105667
cites work: The representation of biregular rings by sheaves
cites work: Lattices With Unique Complements
cites work: The Lattice Theory of Post Algebras
cites work: P-algebras, an abstraction from Post algebras
cites work: Logics Which Are Characterized by Subresiduated Lattices
cites work: Completions of orthomodular lattices. II
cites work: A bundle representation for continuous geometries
cites work: Q3874277
cites work: Q5641137
cites work: Model-completeness for sheaves of structures
cites work: Partially Ordered Sets
cites work: Q5599186
cites work: Q5623714
cites work: Modules over commutative regular rings
cites work: The Theory of Representation for Boolean Algebras
full work available at URL: https://doi.org/10.1007/bf00389840
OpenAlex ID: W1999875661
description: scientific article; zbMATH DE number 947533