|
Normal bases for Hopf-Galois algebras
Author(s):
H.
F.
Kreimer
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2853-2856.
MSC (2000):
Primary 16W30
Posted:
March 14, 2002
MathSciNet review:
1908907
Retrieve article in:
PDF
This article is available free of charge
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  .
References:
-
- 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
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
16W30
Retrieve articles in all Journals with
MSC (2000):
16W30
Additional Information:
H.
F.
Kreimer
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
Email:
kreimer@math.fsu.edu
DOI:
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
Posted:
March 14, 2002
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2002,
American Mathematical Society
|
