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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.

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Gendo-symmetric algebras, canonical comultiplication, bar cocomplex and dominant dimension
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by Ming Fang and Steffen Koenig PDF
Trans. Amer. Math. Soc. 368 (2016), 5037-5055 Request permission


To each endomorphism algebra $A$ of a generator over a symmetric algebra, first a canonical comultiplication (possibly without a counit) is constructed and then a bar cocomplex. The algebras $A$ are characterised by the existence of this data. The dominant dimension of $A$ is shown to be determined by the exactness of the cocomplex at its beginning terms.
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Additional Information
  • Ming Fang
  • Affiliation: Institute of Mathematics, Chinese Academy of Sciences Beijing 100190, People’s Republic of China
  • MR Author ID: 715486
  • Email:
  • Steffen Koenig
  • Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
  • MR Author ID: 263193
  • Email:
  • Received by editor(s): January 22, 2014
  • Received by editor(s) in revised form: June 4, 2014
  • Published electronically: October 5, 2015
  • Additional Notes: The first author was supported by the National Natural Science Foundation of China (No.11001253 and No. 11271318)
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 5037-5055
  • MSC (2010): Primary 16G10, 13E10
  • DOI:
  • MathSciNet review: 3456170