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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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Classifying Serre subcategories of finitely presented modules
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by Grigory Garkusha and Mike Prest PDF
Proc. Amer. Math. Soc. 136 (2008), 761-770 Request permission

Abstract:

Given a commutative coherent ring $R$, a bijective correspondence between the thick subcategories of perfect complexes $\mathcal D_{\operatorname {per}}(R)$ and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of isomorphism classes of indecomposable injective modules are used in an essential way.
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Additional Information
  • Grigory Garkusha
  • Affiliation: Department of Mathematics, Swansea University, SA2 8PP Swansea, United Kingdom
  • MR Author ID: 660286
  • ORCID: 0000-0001-9836-0714
  • Email: G.Garkusha@swansea.ac.uk
  • Mike Prest
  • Affiliation: Department of Mathematics, University of Manchester, Oxford Road, M13 9PL Manchester, United Kingdom
  • MR Author ID: 141975
  • Email: mprest@maths.man.ac.uk
  • Received by editor(s): May 23, 2006
  • Received by editor(s) in revised form: July 5, 2006
  • Published electronically: November 30, 2007
  • Additional Notes: This paper was written during the visit of the first author to the University of Manchester, which was supported by the MODNET Research Training Network in Model Theory. He would like to thank the University for its kind hospitality.
  • Communicated by: Paul Goerss
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 761-770
  • MSC (2000): Primary 13C05, 13C11, 18E30, 18G35
  • DOI: https://doi.org/10.1090/S0002-9939-07-08844-2
  • MathSciNet review: 2361847