Foxby equivalence, complete modules, and torsion modules
type: Item
instance of: scholarly article
title: Foxby equivalence, complete modules, and torsion modules
zbMATH Open document ID: 1010.16009
DOI: 10.1016/S0022-4049(02)00043-9
author: Peter Jørgensen
author: Anders J. Frankild
published in: Journal of Pure and Applied Algebra
publication date: 2002-12-02T00:00:00Z
review text: An equivalence theory for derived categories over differential graded algebras is developed using the adjoint functors and the classes of objects for which the values of unit and counit of adjunction are isomorphisms (Auslander and Bass classes). Some properties of the new equivalence are shown. It is proved that both classical Foxby equivalence (for Noetherian, local, commutative rings) and the Morita equivalence for complete modules and torsion modules, developed by Dwyer and Greenless, arise as special cases. Moreover, a new instance of this theory (Matlis equivalence) gives a characterization of Gorenstein rings.
Mathematics Subject Classification ID: 16E45
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 1839052
zbMATH Keywords: Matlis equivalences
zbMATH Keywords: derived categories
zbMATH Keywords: differential graded algebras
zbMATH Keywords: adjoint functors
zbMATH Keywords: Foxby equivalences
zbMATH Keywords: Morita equivalences
zbMATH Keywords: complete modules
zbMATH Keywords: torsion modules
zbMATH Keywords: Gorenstein rings
reviewed by: A. I. Kashu
MaRDI profile type: Publication
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cites work: Morita Theory for Derived Categories
description: scientific article; zbMATH DE number 1839052