The homomorphism \(M^*\otimes N\to Hom(M,N)\)
type: Item
instance of: scholarly article
title: The homomorphism \(M^*\otimes N\to Hom(M,N)\)
zbMATH Open document ID: 0591.13008
DOI: 10.1007/BF02837253
author: B. George
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
review text: The author proves the following two results: (i) For two non-zero reflexive modules M and N of finite projective dimensions over a Gorenstein local ring for which Hom(M,N) is a module of syzygies, the natural homomorphism \(M^*\otimes N\to Hom(M,N)\) is an isomorphism. (ii) The projective dimension of a module M over a regular local ring \(R \leq n\Leftrightarrow Ext^ n_ R(M,R)\otimes M\to Ext^ n_ R(M,M)\) is surjective, in which case it is actually bijective. The result extends the usual criterion for the projectivity of a module.
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 13C10
zbMATH DE Number: 3948440
zbMATH Keywords: Gorenstein local ring
zbMATH Keywords: module of syzygies
zbMATH Keywords: projectivity
MaRDI profile type: Publication
cites work: Stable module theory
cites work: Maximal Orders
cites work: On the ubiquity of Gorenstein rings
cites work: Q3244153
cites work: On the vanishing of Tor in regular local rings
cites work: Reflexive modules over regular local rings
cites work: A note on grade
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full work available at URL: https://doi.org/10.1007/bf02837253
OpenAlex ID: W2000930554
description: scientific article; zbMATH DE number 3948440