Group-graded rings and duality

Quinn, Declan

doi:10.1090/S0002-9947-1985-0805958-0

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ISSN 1088-6850(online) ISSN 0002-9947(print)

Group-graded rings and duality

Author: Declan Quinn
Journal: Trans. Amer. Math. Soc. 292 (1985), 155-167
MSC: Primary 16A03; Secondary 16A12
MathSciNet review: 805958
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Abstract: We give an alternative construction of the duality between finite group actions and group gradings on rings which was shown by Cohen and Montgomery in [1]. This duality is then used to extend known results on skew group rings to corresponding results for large classes of group-graded rings. Finally we modify the construction slightly to handle infinite groups.

[1] 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 (85i:16002), http://dx.doi.org/10.1090/S0002-9947-1984-0728711-4
[2] Miriam Cohen and Louis H. Rowen, Group graded rings, Comm. Algebra 11 (1983), no. 11, 1253–1270. MR 696990 (85b:16002), http://dx.doi.org/10.1080/00927878308822904
[3] D. S. Passman, It’s essentially Maschke’s theorem, Rocky Mountain J. Math. 13 (1983), no. 1, 37–54. MR 692575 (84e:16023), http://dx.doi.org/10.1216/RMJ-1983-13-1-37
[4] D. S. Passman, Semiprime crossed products, Houston J. Math. 11 (1985), no. 2, 257–267. MR 792201 (86j:16035)
[5] D. S. Passman, Infinite crossed products and group-graded rings, Trans. Amer. Math. Soc. 284 (1984), no. 2, 707–727. MR 743740 (85j:16012), http://dx.doi.org/10.1090/S0002-9947-1984-0743740-2

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