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Cohen–Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras
- Source :
- Journal of Algebra. 288:137-211
- Publication Year :
- 2005
- Publisher :
- Elsevier BV, 2005.
-
Abstract
- We use torsion pairs in stable categories and cotorsion pairs in modules categories to study, in general infinitely generated, Cohen–Macaulay modules and (a generalization of) modules of finite projective or injective dimension over an Artin algebra. We concentrate our investigation to the study of virtually Gorenstein algebras which provide a common generalization of Gorenstein algebras and algebras of finite representation or Cohen–Macaulay type. This class of algebras on the one hand has rich homological structure and satisfies several representation/torsion theoretic finiteness conditions, and on the other hand it is closed under various operations, for instance derived equivalences and stable equivalences of Morita type. In addition virtual Gorensteinness provides a useful tool for the study of the Gorenstein Symmetry Conjecture and modified versions of the Telescope Conjecture for module or stable categories.
- Subjects :
- Cohen–Macaulay modules
Discrete mathematics
Pure mathematics
Algebra and Number Theory
Conjecture
Mathematics::Commutative Algebra
Gorenstein Symmetry Conjecture
Stable categories
Triangulated categories
Covariantly, contravariantly finite and definable subcategories
Injective function
Finite representation
Artin algebra
Gorenstein rings
Torsion pairs and cotorsion pairs
Torsion (algebra)
Artin algebras
Compact objects
Telescope Conjecture
Mathematics
Subjects
Details
- ISSN :
- 00218693
- Volume :
- 288
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra
- Accession number :
- edsair.doi.dedup.....ad1a27ed64855baafba42d00e10ac3c5