Injective modules and semistar operations
type: Item
instance of: scholarly article
title: Injective modules and semistar operations
zbMATH Open document ID: 1238.13008
author: Gabriele Fusacchia
published in: Journal of Pure and Applied Algebra
publication date: 2012-01-24T00:00:00Z
review text: The author classify injective modules over an integral domains by considering the class of semistar noetherian domains. The main result states that if \(*\) is a semistar operation over a domain \(R\), then every injective module \(H\) admits a direct composition \(H=A\bigoplus B\bigoplus C\) where \(A\) is the injective hull of the \(*\)-null part \(\tau_{*}H\), \(B\) is the injective hull of a maximal co-\(*\)-submodule of \(H\) and \(C\) is \(*\)-neutral. Moreover, if \(R\) is \(*\)-noetherian, the structure of \(B\) is described and a complete classification of the injective hulls of co-\(*\)-modules is obtained.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 5999987
zbMATH Keywords: injective module
zbMATH Keywords: semistar Noetherian domain
Wikidata QID: Q114155497
reviewed by: A. Mimouni
MaRDI profile type: Publication
full work available at URL: j.jpaa.2011.05.004
OpenAlex ID: W2167127838
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DOI: 10.1016/J.JPAA.2011.05.004
description: scientific article; zbMATH DE number 5999987