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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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On the projectivity of module coalgebras
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by Siu-Hung Ng PDF
Proc. Amer. Math. Soc. 126 (1998), 3191-3198 Request permission

Abstract:

In this paper, we derive some criteria for the projectivity of a module coalgebra over a finite dimensional Hopf algebra. In particular, we show that any Hopf algebra over a field of characteristic zero is faithfully flat over its group-like subHopf algebra. Finally, we prove that if $B$ is a finite dimensional subHopf algebra of a Hopf algebra $A$, then $B$ is normal in $A$ if and only if $AB^+ = B^+A$. This improves a result by S. Montgomery (1993).
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Additional Information
  • Siu-Hung Ng
  • Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
  • Address at time of publication: Department of Mathematics, University of California at Santa Cruz, Santa Cruz, California 95064
  • MR Author ID: 343929
  • Email: shng@math.ucsc.edu
  • Received by editor(s): September 27, 1996
  • Received by editor(s) in revised form: April 3, 1997
  • Communicated by: Ken Goodearl
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3191-3198
  • MSC (1991): Primary 16W30
  • DOI: https://doi.org/10.1090/S0002-9939-98-04599-7
  • MathSciNet review: 1469428