Star operations on modules
type: Item
instance of: scholarly article
title: Star operations on modules
zbMATH Open document ID: 1173.13025
author: Giampaolo Picozza
author: Said El Baghdadi
published in: Journal of Algebra
publication date: 2009-06-30T00:00:00Z
review text: The authors generalize the theory of (semi)star operations (defined on integral domains) to the case of torsion free modules over integral domains. After listing basic properties, the authors prove that unlike integral domains, semistar operations of finite type on modules do not necessarily induce s localizing system of finite type. Further, they give necessary and sufficient conditions for a semistar operation on a module to be stable. Namely, they prove that for a torsion free \(D\)-module \(M\) and for a a \(D\)-semistar operation \(*\) on \(M\), \(*\) is stable if and only if \(*=*_{\mathcal{F}^{*}}\). The paper closes with a section on star cancellation problem.
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 5572155
zbMATH Keywords: star operation
zbMATH Keywords: semistar operation
zbMATH Keywords: localizing system
zbMATH Keywords: module
reviewed by: A. Mimouni
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.02.004
OpenAlex ID: W1976620661
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DOI: 10.1016/J.JALGEBRA.2009.02.004
description: scientific article; zbMATH DE number 5572155