A dual characterization of subdirectly irreducible BAOs
type: Item
instance of: scholarly article
title: A dual characterization of subdirectly irreducible BAOs
zbMATH Open document ID: 1050.03045
DOI: 10.1023/B:STUD.0000034188.80692.46
author: Yde Venema
published in: Studia Logica
publication date: 2004-08-16T00:00:00Z
review text: Given a Boolean algebra with operators \({\mathbf{A}} = ({\mathbf{B}}_{{\mathbf{A}}} , (f_i)_{i \in I})\), a relation \(R^{\star}\), called the {topo-reachability relation}, is defined on the set \(A_*\) of ultrafilters of \({\mathbf{B}}_{{\mathbf{A}}}\). If \(T_{{{\mathbf{A}}}_*}\) is the collection of those ultrafilters \(u\) of \({\mathbf{B}}_{{\mathbf{A}}}\) such that \(R^{\star}[u] = A_*\), it is proved that \({\mathbf{A}}\) is simple iff \(T_{{\mathbf{A}}_*} = A_*\), and \({\mathbf{A}}\) is subdirectly irreducible iff \(T_{{\mathbf{A}}_*}\) is non-empty and open in \(A_*\) with the Stone topology.
reviewed by: Manuel Abad
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06E25
zbMATH DE Number: 2091573
zbMATH Keywords: Boolean algebras with operators
zbMATH Keywords: subdirect irreducibility
zbMATH Keywords: duality
zbMATH Keywords: ultrafilters
zbMATH Keywords: Stone topology
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2091573