Extension closed reflexive modules
type: Item
instance of: scholarly article
title: Extension closed reflexive modules
zbMATH Open document ID: 0658.16009
DOI: 10.1007/BF01190663
author: Mitsuo Hoshino
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: For a left and right noetherian ring \(R\), we show that both the class of the finitely generated torsionless left \(R\)-modules and the class of the finitely generated reflexive left \(R\)-modules are closed under extensions if and only if for \(i=1,2\) the functor \(\mathrm{Ext}_ R^{i-1}(\mathrm{Ext}^ i_ R(-,R),R)\) vanishes on the finitely generated right \(R\)-modules. As a particular case, we get the following: A commutative noetherian local domain \(R\) of Krull dimension two is a Cohen-Macaulay ring whenever the class of the finitely generated reflexive \(R\)-modules is closed under extensions.
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16S20
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 4075311
zbMATH Keywords: left and right noetherian ring
zbMATH Keywords: finitely generated reflexive left R- modules
zbMATH Keywords: extensions
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: reflexive R-modules
MaRDI profile type: Publication
cites work: Q5586467
cites work: Injective Dimension in Noetherian Rings
cites work: On the ubiquity of Gorenstein rings
cites work: Der kanonische Modul eines Cohen-Macaulay-Rings. (The canonical moduls of a Cohen-Macaulay-ring)
cites work: Duality in Noetherian Rings
full work available at URL: https://doi.org/10.1007/bf01190663
OpenAlex ID: W2062059557
Recommended article: Q4883250
Recommended article: Q4011397
Recommended article: Extension closure of relative syzygy modules.
Recommended article: Q3338399
Recommended article: INTEGRALLY CLOSED MODULES
Recommended article: Totally reflexive extensions and modules.
Recommended article: A characterisation of reflexive modules
Recommended article: On extensions of modules
Recommended article: Modules of existentially closed algebras
description: scientific article; zbMATH DE number 4075311