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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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Normal bases for Hopf-Galois algebras
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by H. F. Kreimer PDF
Proc. Amer. Math. Soc. 130 (2002), 2853-2856 Request permission

Abstract:

Let $H$ be a Hopf algebra over a commutative ring $R$ such that $H$ is a finitely generated, projective module over $R$, let $A$ be a right $H$-comodule algebra, and let $B$ be the subalgebra of $H$-coinvariant elements of $A$. If $A$ is a Galois extension of $B$ and $B$ is a local subalgebra of the center of $A$, then $A$ is a cleft right $H$-comodule algebra or, equivalently, there is a normal basis for $A$ over $B$.
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Additional Information
  • H. F. Kreimer
  • Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
  • Email: kreimer@math.fsu.edu
  • Received by editor(s): April 11, 2001
  • Received by editor(s) in revised form: May 23, 2001
  • Published electronically: March 14, 2002
  • Communicated by: Martin Lorenz
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 2853-2856
  • MSC (2000): Primary 16W30
  • DOI: https://doi.org/10.1090/S0002-9939-02-06442-0
  • MathSciNet review: 1908907