On Gorenstein rings
type: Item
instance of: scholarly article
title: On Gorenstein rings
zbMATH Open document ID: 0634.16008
DOI: 10.1007/BF01161633
author: Overtoun M. G. Jenda
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183721
review text: If R is noetherian, injective resolvents can be constructed. In this paper, it is shown that every injective resolvent \(...\to E_ 1\to E_ 0\to M\to 0\) is exact at \(E_ i\), \(i\geq n-1\), if and only if R is Gorenstein of dimension at most n. Additional characterizations of such rings are discussed. Finally, syzygies for injective resolvents are characterized in the case R is Gorenstein of dimension at most 1.
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16E10
zbMATH DE Number: 4031893
zbMATH Keywords: noetherian ring
zbMATH Keywords: Gorenstein ring
zbMATH Keywords: injective dimension
zbMATH Keywords: flat dimension
zbMATH Keywords: injective resolvents
zbMATH Keywords: syzygies
MaRDI profile type: Publication
cites work: Injective and flat covers, envelopes and resolvents
cites work: Balanced functors applied to modules
cites work: Rings with Ascending Condition on Annihilators
cites work: Direct-sum representations of injective modules
cites work: Q3722606
cites work: INJECTIVE RESOLVENTS AND PREENVELOPES
cites work: Divisible Modules
cites work: Absolutely Pure Modules
cites work: Q3882615
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description: scientific article; zbMATH DE number 4031893