Tilting objects in abelian categories and quasitilted rings |
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Authors: | Riccardo Colpi Kent R. Fuller |
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Affiliation: | Department of Pure and Applied Mathematics, University of Padova, via Belzoni 7, I 35100 Padova, Italy ; Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419 |
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Abstract: | D. Happel, I. Reiten and S. Smalø initiated an investigation of quasitilted artin -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 . Here, employing a notion of -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. |
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