Normal bases for Hopf-Galois algebras
HTML articles powered by AMS MathViewer
- 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 $B$.References
- Nicolas Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR 0360549
- Yukio Doi and Mitsuhiro Takeuchi, Cleft comodule algebras for a bialgebra, Comm. Algebra 14 (1986), no. 5, 801–817. MR 834465, DOI 10.1080/00927878608823337
- H. F. Kreimer and P. M. Cook II, Galois theories and normal bases, J. Algebra 43 (1976), no. 1, 115–121. MR 424782, DOI 10.1016/0021-8693(76)90146-0
- H. F. Kreimer and M. Takeuchi, Hopf algebras and Galois extensions of an algebra, Indiana Univ. Math. J. 30 (1981), no. 5, 675–692. MR 625597, DOI 10.1512/iumj.1981.30.30052
- Dmitriy Rumynin, Hopf-Galois extensions with central invariants and their geometric properties, Algebr. Represent. Theory 1 (1998), no. 4, 353–381. MR 1683618, DOI 10.1023/A:1009944607078
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