Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Tilting objects in abelian categories and quasitilted rings
HTML articles powered by AMS MathViewer

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
Similar Articles
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