Inner gradings and Galois extensions with normal basis
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- by Margaret Beattie PDF
- Proc. Amer. Math. Soc. 107 (1989), 881-886 Request permission
Abstract:
We prove that for $G$ a finite group, a $G$-graded Azumaya algebra over a commutative ring has inner grading if and only if an associated Galois extension has normal basis.References
- Margaret Beattie, A direct sum decomposition for the Brauer group of $H$-module algebras, J. Algebra 43 (1976), no. 2, 686–693. MR 441942, DOI 10.1016/0021-8693(76)90134-4
- Robert J. Blattner and Susan Montgomery, Crossed products and Galois extensions of Hopf algebras, Pacific J. Math. 137 (1989), no. 1, 37–54. MR 983327
- Stephen U. Chase and Moss E. Sweedler, Hopf algebras and Galois theory, Lecture Notes in Mathematics, Vol. 97, Springer-Verlag, Berlin-New York, 1969. MR 0260724
- L. N. Childs, G. Garfinkel, and M. Orzech, The Brauer group of graded Azumaya algebras, Trans. Amer. Math. Soc. 175 (1973), 299–326. MR 349652, DOI 10.1090/S0002-9947-1973-0349652-3
- M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258. MR 728711, DOI 10.1090/S0002-9947-1984-0728711-4
- 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
- Morris Orzech and Charles Small, The Brauer group of commutative rings, Lecture Notes in Pure and Applied Mathematics, Vol. 11, Marcel Dekker, Inc., New York, 1975. MR 0457422
- James Osterburg and Declan Quinn, A Noether Skolem theorem for group-graded rings, J. Algebra 113 (1988), no. 2, 483–490. MR 929775, DOI 10.1016/0021-8693(88)90174-3
- Moss Eisenberg Sweedler, Cohomology of algebras over Hopf algebras, Trans. Amer. Math. Soc. 133 (1968), 205–239. MR 224684, DOI 10.1090/S0002-9947-1968-0224684-2
- Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 881-886
- MSC: Primary 16A16; Secondary 16A03, 16A74
- DOI: https://doi.org/10.1090/S0002-9939-1989-0975632-8
- MathSciNet review: 975632