Normal bases for Hopf-Galois algebras

Author:
H. F. Kreimer

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2853-2856

MSC (2000):
Primary 16W30

DOI:
https://doi.org/10.1090/S0002-9939-02-06442-0

Published electronically:
March 14, 2002

MathSciNet review:
1908907

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Hopf algebra over a commutative ring such that is a finitely generated, projective module over , let be a right -comodule algebra, and let be the subalgebra of -coinvariant elements of . If is a Galois extension of and is a local subalgebra of the center of , then is a cleft right -comodule algebra or, equivalently, there is a normal basis for over .

**1.**N. Bourbaki, Elements of Mathematics,*Commutative Algebra*, Hermann, Paris, 1972. MR**50:12997****2.**Y. Doi and M. Takeuchi,*Cleft comodule algebras for a bialgebra*, Comm. in Algebra**14(5)**(1986), 801-817. MR**87e:16025****3.**H.F. Kreimer and P.M. Cook III,*Galois theories and normal bases*, J. Algebra**43**(1976), 115-121. MR**54:12740****4.**H.F. Kreimer and M. Takeuchi,*Hopf algebras and Galois extensions of an algebra*, Indiana U. Math. J.**30**(1981), 675-692. MR**83h:16015****5.**D. Rumynin,*Hopf-Galois extensions with central invariants and their geometric properties*, Algebras and Representation Theory**1**(1998), 353-381. MR**2000h:16051**

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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:
https://doi.org/10.1090/S0002-9939-02-06442-0

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