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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Artinian Hopf algebras are finite dimensional


Authors: Chia-Hsin Liu and James J. Zhang
Journal: Proc. Amer. Math. Soc. 135 (2007), 1679-1680
MSC (2000): Primary 16W30
Published electronically: February 6, 2007
MathSciNet review: 2286075
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Abstract: We prove that an artinian Hopf algebra over a field is finite dimensional. This answers a question of Bergen.


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Additional Information

Chia-Hsin Liu
Affiliation: Department of Mathematics, National Taiwan Normal University, 88 Sec. 4, Ting Chou Road, Taipei, Taiwan, ROC
Email: chliu@math.ntnu.edu.tw

James J. Zhang
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
Email: zhang@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08711-4
PII: S 0002-9939(07)08711-4
Received by editor(s): February 18, 2006
Received by editor(s) in revised form: March 10, 2006
Published electronically: February 6, 2007
Additional Notes: The first author’s research was partially supported by the NSC of ROC
The second author’s research was partially supported by the NSF
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.