Quasidualizing modules
type: Item
instance of: scholarly article
title: Quasidualizing modules
zbMATH Open document ID: 1304.13031
DOI: 10.1216/JCA-2014-6-2-209
author: Bethany Kubik
published in: Journal of Commutative Algebra
publication date: 2014-09-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1202.0745
full work available at URL: https://projecteuclid.org/euclid.jca/1407790530
Mathematics Subject Classification ID: 13D07
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 13J10
zbMATH DE Number: 6340274
zbMATH Keywords: quasidualizing
zbMATH Keywords: semidualizing
zbMATH Keywords: matlis duality
reviewed by: Javier Majadas
MaRDI profile type: Publication
arXiv ID: 1202.0745
cites work: Q5563439
cites work: Q4380359
cites work: Relative homological algebra
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cites work: On injective modules and flat modules
cites work: Homology of Artinian and Matlis reflexive modules. I.
cites work: Q3992979
cites work: An introduction to homological algebra
cites work: Q4049187
review text: Let \(A\) be a commutative noetherian local ring. An \(A\)-module of finite type \(C\) is called semidualizing if the homothety homomorphism \(A \to \)Hom\(_A(C,C)\) is an isomorphism and Ext\(^{>0}_A(C,C)=0\). In this paper the Matlis duals of semidualizing modules are identified as the artinian modules \(M\) such that \(\hat{A} \to \)Hom\(_A(M,M)\) is an isomorphism and Ext\(^{>0}_A(M,M)=0\), where \(\hat{A}\) is the completion of the local ring \(A\). Some properties and variants are also explored.
description: scientific article; zbMATH DE number 6340274