Auslander-Reiten triangles, Ziegler spectra and Gorenstein rings
type: Item
instance of: scholarly article
title: Auslander-Reiten triangles, Ziegler spectra and Gorenstein rings
zbMATH Open document ID: 1082.18010
author: Apostolos Beligiannis
published in: \(K\)-Theory
publication date: 2005-04-07T00:00:00Z
review text: The paper under review is a quite abstract approach to the theory of Auslander-Reiten triangles in triangulated categories. The method is based on the representability of certain functors. The author then defines the Ziegler spectrum for triangulated categories, analogously as it was defined for module categories by \textit{H. Krause, M. Prest} and others. Using this the author interprets the existence of Auslander-Reiten triangles in this topological framework.
reviewed by: Alexander Zimmermann
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 18E40
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 18E10
Mathematics Subject Classification ID: 18F30
zbMATH DE Number: 2153878
zbMATH Keywords: Auslander-Reiten triangles
zbMATH Keywords: compact and pure-injective objects
zbMATH Keywords: Gorenstein rings
zbMATH Keywords: Grothendieck groups
zbMATH Keywords: purity
zbMATH Keywords: Serre functors
zbMATH Keywords: triangulated and derived categories
zbMATH Keywords: Ziegler spectrum
zbMATH Keywords: pure-injectivity
MaRDI profile type: Publication
DOI: 10.1023/B:KTHE.0000035051.14067.EB
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description: scientific article; zbMATH DE number 2153878