Prime elements of non-integral quantales and their applications.
type: Item
instance of: scholarly article
title: Prime elements of non-integral quantales and their applications.
zbMATH Open document ID: 1329.06008
author: Ulrich Höhle
published in: Order
publication date: 2015-11-09T00:00:00Z
review text: The first three sections of this well-written article provide a very readable introduction to quantales, culminating in the question: Which type of space corresponds to a spatial quantale? Towards answering that question, the author introduces in section 4 the involutive semi-integral quantale \(Q(2)\), and relates it to prime elements. The answer to the question is then explained in section 5, using multi valued topologies, summarized as Fact II: Semiunital spatial quantales and \(Q(2)\)-valued sober spaces are equivalent concepts. The final section gives an application to the topologization of the spectrum of \(C^*\)-algebras.
reviewed by: Ittay Weiss
Mathematics Subject Classification ID: 06F07
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 6506232
zbMATH Keywords: semi-integral quantales
zbMATH Keywords: spatial quantales
zbMATH Keywords: many-valued topology
zbMATH Keywords: prime elements
zbMATH Keywords: pure states
zbMATH Keywords: involutive quantales
MaRDI profile type: Publication
full work available at URL: s11083-014-9334-8
OpenAlex ID: W2022822283
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DOI: 10.1007/S11083-014-9334-8
description: scientific article; zbMATH DE number 6506232