\(h\)-divisible modules over integral domains
type: Item
instance of: scholarly article
title: \(h\)-divisible modules over integral domains
zbMATH Open document ID: 1228.13018
author: Sang Bum Lee
published in: Journal of Algebra
publication date: 2011-07-25T00:00:00Z
review text: Let \(R\) be an integral domain which is not a field. In several previous papers, the author proved that there exist the following irreversible implications: \(\,h\)-divisible pure injective \(\Longrightarrow\) weak injective \(\Longrightarrow\) \(\,h\)-divisible. In Section 2 of the paper it is proved that it suffices to use these modules to determine the weak dimension of modules via Tor. In Section 3 various cotorsion modules which are \(\,h\)-divisible are considered, a series of irreversible implications between these modules are established, and characterizations of domains over which some particular implications are reversible. In Section 4 the author introduces copure-weak-injective modules as being those \(R\)-modules \(M\) for which Ext\(^1_R(D,M)=0\) for all weak-injective \(R\)-modules \(D\), and characterizes them over particular domains.
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13D07
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 5931636
zbMATH Keywords: h-divisible module
zbMATH Keywords: pure-injective module
zbMATH Keywords: weak injective module
zbMATH Keywords: flat module
zbMATH Keywords: Matlois domain
zbMATH Keywords: cotorsion module
reviewed by: Toma Albu
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.11.008
OpenAlex ID: W2043062034
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DOI: 10.1016/J.JALGEBRA.2010.11.008
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description: scientific article; zbMATH DE number 5931636