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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Recollements of abelian categories and ideals in heredity chains—a recursive approach to quasi-hereditary algebras
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by Nan Gao, Steffen Koenig and Chrysostomos Psaroudakis PDF
Proc. Amer. Math. Soc. 147 (2019), 4625-4637 Request permission

Abstract:

Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel’s characterisation of idempotent ideals occurring in heredity chains, which in turn characterises quasi-hereditary algebras recursively. Further applications are given to hereditary algebras and to Morita context rings.
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Additional Information
  • Nan Gao
  • Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
  • MR Author ID: 833788
  • Email: nangao@shu.edu.cn
  • Steffen Koenig
  • Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
  • MR Author ID: 263193
  • Email: skoenig@mathematik.uni-stuttgart.de
  • Chrysostomos Psaroudakis
  • Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
  • Address at time of publication: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
  • MR Author ID: 1041820
  • Email: chpsaroud@math.auth.gr
  • Received by editor(s): April 25, 2018
  • Received by editor(s) in revised form: February 10, 2019
  • Published electronically: July 1, 2019
  • Additional Notes: The first named author was supported by the National Natural Science Foundation of China (grant No. 11771272)
    The third named author was supported by Deutsche Forschungsgemeinschaft (DFG, grant KO $1281/14-1$)
  • Communicated by: Jerzy Weyman
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4625-4637
  • MSC (2010): Primary 16G10; Secondary 17B10, 16E60, 18G15
  • DOI: https://doi.org/10.1090/proc/14620
  • MathSciNet review: 4011500