On a theorem of Cohen and Montgomery
Author: Michel Van den Bergh
Journal: Proc. Amer. Math. Soc. 94 (1985), 562-564
MSC: Primary 16A21; Secondary 16A26
MathSciNet review: 792260
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Abstract: In a recent paper, Cohen and Montgomery proved a conjecture of Bergman concerning the relation between the Jacobson radical and the graded Jacobson radical of a ring graded by a finite group. In their proof they made use of the theory of Hopf algebras. In this note we give a short and elementary proof of the Bergman conjecture.
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-  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, https://doi.org/10.1090/S0002-9947-1984-0728711-4
-  D. S. Passman, It’s essentially Maschke’s theorem, Rocky Mountain J. Math. 13 (1983), no. 1, 37–54. MR 692575, https://doi.org/10.1216/RMJ-1983-13-1-37
- Bergman, Groups acting on rings, group graded rings and beyond (Preprint).
- 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)
- D. S. Passman, It's essentially Mascke's theorem, Rocky Mountain J. Math. 13 (1983), 37-54. MR 692575 (84e:16023)