Some properties of Butler modules over valuation domains
type: Item
instance of: scholarly article
title: Some properties of Butler modules over valuation domains
zbMATH Open document ID: 0748.13004
author: Elisabetta Monari Martinez
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1992-06-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108215
review text: A torsion-free module \(B\) over a valuation domain \(R\) is a Butler module if for every torsion \(R\)-module \(T\) and for every exact sequence \(0\to T\to M\to B\to 0\) the induced map \(\text{Hom}(J/I,M)\to\text{Hom}(J/I,B)\) is surjective for all pairs \(I\subset J\) of \(R\)-submodules of the field of quotients of \(R\). The main result of the paper is: For any pure submodule \(N\) of rank \(k\) (=cardinal) of a reduced Butler module \(B\) and any rank one \(k'\)-generated module \(J\) with \(k'>k\), each epimorphism \(N\to J\) splits. This result leads to definitions of two classes of modules ( striped modules and modules having torsion extension property) which also are studied.
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13F30
Mathematics Subject Classification ID: 13C12
Mathematics Subject Classification ID: 18A20
zbMATH DE Number: 20848
zbMATH Keywords: valuation domain
zbMATH Keywords: Butler module
zbMATH Keywords: Hom
zbMATH Keywords: pure submodule
zbMATH Keywords: striped modules
zbMATH Keywords: torsion extension
reviewed by: Stanisław Balcerzyk
MaRDI profile type: Publication
cites work: Infinite Rank Butler Groups
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cites work: Q3699812
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description: scientific article; zbMATH DE number 20848