Reflexive modules and rings with self-injective dimension two
type: Item
instance of: scholarly article
title: Reflexive modules and rings with self-injective dimension two
zbMATH Open document ID: 0696.16007
author: Mitsuo Hoshino
published in: Tsukuba Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author considers the question: When is every finitely generated left module M over a left and right noetherian ring R with \(Ext^ i_ R(M,R)=0\) reflexive for \(i=1,2?\) As main result it is shown that if R is a left and right noetherian ring, then \(inj\dim_ RR=inj\dim R_ R\leq 2\) if and only if for a finitely generated left R-module M the following conditions are equivalent: (1) M is reflexive. (2) There is an exact sequence \(0\to M\to P_ 1\to P_ 0\) of left R-modules with the \(P_ i\) projective. (3) \(Ext^ i_ R(M,R)=0\) for \(i=1,2\). The author also obtains a result for commutative noetherian rings concerning Gorenstein rings.
reviewed by: Dinh Van Huynh
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16D80
zbMATH DE Number: 4139960
zbMATH Keywords: finitely generated left module
zbMATH Keywords: left and right noetherian ring
zbMATH Keywords: Gorenstein rings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496161164
OpenAlex ID: W1569866918
Wikidata QID: Q114047170
DOI: 10.21099/TKBJM/1496161164
description: scientific article; zbMATH DE number 4139960