## Tilting objects in abelian categories and quasitilted rings

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- by Riccardo Colpi and Kent R. Fuller PDF
- Trans. Amer. Math. Soc.
**359**(2007), 741-765 Request permission

## Abstract:

D. Happel, I. Reiten and S. Smalø initiated an investigation of quasitilted artin $K$-algebras that are the endomorphism rings of tilting objects in hereditary abelian categories whose Hom and Ext groups are all finitely generated over a commutative artinian ring $K$. Here, employing a notion of $\ast$-objects, tilting objects in arbitrary abelian categories are defined and are shown to yield a version of the classical tilting theorem between the category and the category of modules over their endomorphism rings. This leads to a module theoretic notion of quasitilted rings and their characterization as endomorphism rings of tilting objects in hereditary cocomplete abelian categories.## References

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## Additional Information

**Riccardo Colpi**- Affiliation: Department of Pure and Applied Mathematics, University of Padova, via Belzoni 7, I 35100 Padova, Italy
- Email: colpi@math.unipd.it
**Kent R. Fuller**- Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419
- Email: kfuller@math.uiowa.edu
- Received by editor(s): September 21, 2004
- Received by editor(s) in revised form: December 3, 2004
- Published electronically: August 24, 2006
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**359**(2007), 741-765 - MSC (2000): Primary 16E10, 16G99, 16S50, 18E40, 18E25, 18G20; Secondary 16B50, 16D90
- DOI: https://doi.org/10.1090/S0002-9947-06-03909-2
- MathSciNet review: 2255195