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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Hochschild homology and truncated cycles
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by Petter Andreas Bergh, Yang Han and Dag Madsen PDF
Proc. Amer. Math. Soc. 140 (2012), 1133-1139 Request permission


We study algebras having $2$-truncated cycles and show that these algebras have infinitely many nonzero Hochschild homology groups. Consequently, algebras of finite global dimension have no $2$-truncated cycles and therefore satisfy a higher version of the “no loops conjecture”.
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Additional Information
  • Petter Andreas Bergh
  • Affiliation: Institutt for Matematiske FAG, NTNU, N-7491 Trondheim, Norway
  • MR Author ID: 776982
  • Email:
  • Yang Han
  • Affiliation: KLMM, AMSS, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
  • Email:
  • Dag Madsen
  • Affiliation: Department of Mathematics, 215 Carnegie, Syracuse University, Syracuse, New York 13244-1150
  • Address at time of publication: Profesjonshøgskolen, Universitetet i Nordland, 8049 Bodø, Norway
  • MR Author ID: 639380
  • Email:,
  • Received by editor(s): July 12, 2010
  • Received by editor(s) in revised form: October 27, 2010, and November 26, 2010
  • Published electronically: November 23, 2011
  • Additional Notes: The first author was supported by NFR Storforsk grant No. 167130
    The second author was supported by Project 10731070 NSFC

  • Dedicated: Dedicated to Professor Claus Michael Ringel on the occasion of his 65th birthday
  • Communicated by: Birge Huisgen-Zimmermann
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1133-1139
  • MSC (2010): Primary 16E40
  • DOI:
  • MathSciNet review: 2869099