Free modules over Hjelmslev rings in which not every maximal linearly independent subset is a basis
type: Item
instance of: scholarly article
title: Free modules over Hjelmslev rings in which not every maximal linearly independent subset is a basis
zbMATH Open document ID: 0765.51004
DOI: 10.1007/BF01225769
published in: Journal of Geometry
publication date: 1993-01-17T00:00:00Z
review text: It is proved that for an \(H\)-ring \(R\), every maximal linearly independent subset of a free left \(R\)-module \(V\) is a basis of \(V\) if and only if \(R\) is left-noetherian or \(V\) is finitely generated. As a consequence the incidence structure \((P,{\mathcal L})\) with \(\rho=\rho(V^*)\) and \({\mathcal L}=\{\rho(U\backslash Q)| U\) is a free submodule of \(V\) with \(\dim U=2\}\), where \(R\) is an \(H\)-ring with maximal ideal \(N\) and \(V\) an \(R\)- module with torsion \(Q\), \(R^*=R\backslash N\), \(V^*=V\backslash Q\) and \(\rho:V^*\to V^*/R^*:x\mapsto R^*x\) the canonical epimorphism, is a projective Hjelmslev space iff \(R\) is left-noetherian or \(V\) is finitely generated.
reviewed by: Dirk Keppens
Mathematics Subject Classification ID: 51C05
Mathematics Subject Classification ID: 16P40
zbMATH DE Number: 98732
zbMATH Keywords: \(H\)-rings
zbMATH Keywords: projective Hjelmslev spaces
zbMATH Keywords: modules over \(AH\)-rings
author: Alexander Kreuzer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 98732