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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equivalences induced by infinitely generated tilting modules


Author: Silvana Bazzoni
Journal: Proc. Amer. Math. Soc. 138 (2010), 533-544
MSC (2000): Primary 16D90, 16E30, 18E30; Secondary 16S90, 16G10
Published electronically: October 7, 2009
MathSciNet review: 2557170
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Abstract: We generalize Brenner and Butler's Theorem as well as Happel's Theorem on the equivalences induced by a finitely generated tilting module over Artin algebras, to the case of an infinitely generated tilting module over an arbitrary associative ring establishing the equivalences induced between subcategories of module categories and also at the level of derived categories.


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Additional Information

Silvana Bazzoni
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35121 Padova, Italy
Email: bazzoni@math.unipd.it

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10120-X
PII: S 0002-9939(09)10120-X
Keywords: Tilting modules, equivalences and derived equivalences.
Received by editor(s): October 8, 2008
Received by editor(s) in revised form: July 2, 2009
Published electronically: October 7, 2009
Additional Notes: Supported by MIUR, PRIN 2005, project “Perspectives in the theory of rings, Hopf algebras and categories of modules” and by Università di Padova (Progetto di Ateneo CPDA071244/07 “Algebras and cluster categories”).
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.