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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
DOI: https://doi.org/10.1090/S0002-9939-07-08711-4
Published electronically: February 6, 2007
MathSciNet review: 2286075
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that an artinian Hopf algebra over a field is finite dimensional. This answers a question of Bergen.


References [Enhancements On Off] (What's this?)

  • [Co] I.G. Connell, On the group ring, Canad. J. Math. 15 (1963), 650-685.MR 0153705 (27:3666)
  • [DNR] S. Dascalescu, C. Nastasescu, and S. Raianu, Hopf algebras, An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, vol. 235, Marcel Dekker, Inc., New York, 2001. MR 1786197 (2001j:16056)
  • [GK] A. Goldie and G. Krause, Artinian quotient rings of ideal invariant Noetherian rings, J. Algebra 63 (1980), no. 2, 374-388. MR 0570719 (81h:16007)
  • [JR] S.K. Jain and S.T. Rizvi (eds.), Ring theory, Proceedings of the Twenty-first Biennial Ohio State-Denison Mathematics Conference held at Denison University, Granville, Ohio, May 14-16, 1992. World Scientific Publishing Co., Inc., River Edge, NJ, 1993. MR 1344218 (96d:16001)
  • [Le] T.-K. Lee, private communication, 2003.
  • [LZ] C.-H. Liu and J.J. Zhang, private notes, 2001.
  • [MR] J. C. McConnell and J. C . Robson, Noncommutative Noetherian Rings, Wiley, Chichester, 1987.MR 0934572 (89j:16023)
  • [Sw] M.E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485 (40:5705)

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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: https://doi.org/10.1090/S0002-9939-07-08711-4
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.

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