The ring of \(\alpha \)-quotients.
type: Item
instance of: scholarly article
title: The ring of \(\alpha \)-quotients.
zbMATH Open document ID: 1063.54028
author: Anthony W. Hager
author: Jorge Martinez
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: The paper introduces, for each regular, uncountable cardinal \(\alpha \), the ring of quotients of the commutative ring \(\mathcal A\) obtained by the direct limit \[ {\mathcal Q}_{\alpha }\mathcal A=\varinjlim\Hom_{\mathcal A}(I,{\mathcal A}), \] where \(I\) ranges over the filter of base of ideals which can be generated by fewer than \(\alpha \) elements of \(\mathcal A\), the so-called ring of \(\alpha \)-quotients. It is shown that \(\mathcal Q_{\alpha }\mathcal A\) is the least \(\alpha \)-selfinjective ring of quotients of \(\mathcal A\). For semiprime rings, \(\mathcal Q_{\alpha }\mathcal A\) has the \(\alpha \)-splitting property. The results are applied namely to archimedean \(f\)-rings.
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 54G05
Mathematics Subject Classification ID: 13B30
Mathematics Subject Classification ID: 06F25
zbMATH DE Number: 2158773
zbMATH Keywords: \(\alpha \)-splitting property
zbMATH Keywords: \(\alpha \)-cloz spaces
zbMATH Keywords: \(\alpha \)-annihilator
MaRDI profile type: Publication
full work available at URL: s00012-002-8182-3
OpenAlex ID: W2318286964
DOI: 10.1007/S00012-002-8182-3
description: scientific article; zbMATH DE number 2158773