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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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Maximal $n$-orthogonal modules for selfinjective algebras
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by Karin Erdmann and Thorsten Holm PDF
Proc. Amer. Math. Soc. 136 (2008), 3069-3078 Request permission

Abstract:

Let $A$ be a finite-dimensional selfinjective algebra. We show that, for any $n\ge 1$, maximal $n$-orthogonal $A$-modules (in the sense of Iyama) rarely exist. More precisely, we prove that if $A$ admits a maximal $n$-orthogonal module, then all $A$-modules are of complexity at most 1.
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Additional Information
  • Karin Erdmann
  • Affiliation: Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
  • MR Author ID: 63835
  • ORCID: 0000-0002-6288-0547
  • Email: erdmann@maths.ox.ac.uk
  • Thorsten Holm
  • Affiliation: Institut für Algebra und Geometrie, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany – and – Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
  • Address at time of publication: Leibniz Universität Hannover, Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Welfengarten 1, 30167 Hannover, Germany
  • Email: thorsten.holm@mathematik.uni-magdeburg.de, holm@math.uni-hannover.de
  • Received by editor(s): August 8, 2006
  • Received by editor(s) in revised form: July 20, 2007
  • Published electronically: April 29, 2008
  • Additional Notes: We gratefully acknowledge the support of the Mathematisches Forschungsinstitut Oberwolfach through a Research in Pairs (RiP) project, and also the support through a London Mathematical Society Scheme 4 grant.
  • Communicated by: Birge Huisgen-Zimmermann
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3069-3078
  • MSC (2000): Primary 16G10, 16D50, 16E10, 16G70
  • DOI: https://doi.org/10.1090/S0002-9939-08-09297-6
  • MathSciNet review: 2407069