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Inner gradings and Galois extensions with normal basis


Author: Margaret Beattie
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
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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.


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  • [1] M. Beattie, A direct sum decomposition for the Brauer group of $ H$-module algebras, J. Alg. 43 (1976), 686-693. MR 0441942 (56:333)
  • [2] R. J. Blattner and S. Montgomery, Crossed products and Galois extensions of Hopf algebras, Pacific J. Math. 137 (1989), 37-54. MR 983327 (90a:16007)
  • [3] S. U. Chase and M. E. Sweedler, Hopf algebras and Galois theory, Lecture Notes in Math. 97, Springer-Verlag, Berlin, 1969. MR 0260724 (41:5348)
  • [4] L. N. Childs, G. Garfinkel and M. Orzech, The Brauer group of graded Azumaya algebras, Trans. Amer. Math. Soc. 175 (1973), 299-325. MR 0349652 (50:2145)
  • [5] M. Cohen and S. Montgomery, Group graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), 237-258. MR 728711 (85i:16002)
  • [6] H. F. Kreimer and P. M. Cook II, Galois theories and normal bases, J. Alg. 43 (1976), 115-121. MR 0424782 (54:12740)
  • [7] M. Orzech and C. Small, The Brauer group of commutative rings, Lecture Notes in Pure and Appl. Math., No. 11, Marcel Dekker, New York, 1975. MR 0457422 (56:15627)
  • [8] J. Osterburg and D. Quinn, A Noether Skolem theorem for group-graded rings, J. Alg. 113 (1988), 483-490; Addendum, J. Alg. 120 (1989), 414-415. MR 929775 (88m:16001)
  • [9] M. E. Sweedler, Cohomology of algebras over Hopf algebras, Trans. Amer. Math. Soc. 133 (1968), 205-239. MR 0224684 (37:283)
  • [10] -, Hopf algebras, Benjamin, New York, 1969. MR 0252485 (40:5705)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0975632-8
Article copyright: © Copyright 1989 American Mathematical Society

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