Cotorsion pairs induced by duality pairs
type: Item
instance of: scholarly article
title: Cotorsion pairs induced by duality pairs
zbMATH Open document ID: 1184.13042
DOI: 10.1216/JCA-2009-1-4-621
author: Henrik Holm
author: Peter Jørgensen
published in: Journal of Commutative Algebra
publication date: 2010-02-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/0905.0776
review text: \textit{L. L.\ Avramov} and \textit{H.-B.\ Foxby} [Proc.\ Lond. Math.\ Soc., III. Ser. 75, 241--270 (1997; Zbl 0901.13011)] and \textit{L. W.\ Christensen} [Trans.\ Am.\ Soc.\ 353, No. 5, 1839--1883 (2001; Zbl 0969.13006)] demonstrated how a semidualizing complex \(C\) over a commutative ring \(R\) gives rise to the so-called Auslander class \(A^C_0\) and the Bass class \(B^C_0\). The authors introduce \textit{duality pairs} parts of which are \(A^C_0\) and \(B^C_0\) and show how the left of such a pair is covering and preenveloping. Then, a result of \textit{E. E. Enochs} and \textit{H. Holm} [Isr. J.\ Math.\ 174, 253--268 (2009; Zbl 1184.13029)] on Auslander and Bass classes is generalized: \textit{the class of Gorenstein injective modules is covering when the ground ring has a dualizing complex.}
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13D07
Mathematics Subject Classification ID: 18G25
zbMATH DE Number: 5673549
zbMATH Keywords: Auslander class
zbMATH Keywords: Bass class
zbMATH Keywords: cotorsion pair
zbMATH Keywords: cover
zbMATH Keywords: duality pair
zbMATH Keywords: Gorenstein flat dimension
zbMATH Keywords: Gorenstein injective dimension
zbMATH Keywords: preenvelope
zbMATH Keywords: semidualizing complex
Wikidata QID: Q105783642
reviewed by: Marek Golasiński
MaRDI profile type: Publication
arXiv ID: 0905.0776
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description: scientific article