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

 

Normal bases for Hopf-Galois algebras


Author: H. F. Kreimer
Journal: Proc. Amer. Math. Soc. 130 (2002), 2853-2856
MSC (2000): Primary 16W30
Published electronically: March 14, 2002
MathSciNet review: 1908907
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06442-0
PII: S 0002-9939(02)06442-0
Keywords: Cleft Hopf algebra, normal basis
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
Article copyright: © Copyright 2002 American Mathematical Society