Smash products and $G$-Galois actions
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- by James Osterburg PDF
- Proc. Amer. Math. Soc. 98 (1986), 217-221 Request permission
Abstract:
We show that duality for coactions follows because the smash product is a $G$-Galois extension. We study $X$-inner and $X$-outer actions of the smash product and prove that if $A$ is a semiprime $G$-graded ring such that $G$ is $X$-outer on the smash product then the center of $A$ is contained in the homogeneous component of the identity element of $G$.References
- 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
- F. R. DeMeyer, Some notes on the general Galois theory of rings, Osaka Math. J. 2 (1965), 117–127. MR 182645
- J.-M. Goursaud, J.-L. Pascaud, and J. Valette, Sur les travaux de V. K. Kharchenko, Paul Dubreil and Marie-Paule Malliavin Algebra Seminar, 34th Year (Paris, 1981) Lecture Notes in Math., vol. 924, Springer, Berlin-New York, 1982, pp. 322–355 (French). MR 662266
- Yoshimi Kitamura, Note on the maximal quotient ring of a Galois subring, Math. J. Okayama Univ. 19 (1976/77), no. 1, 55–60. MR 435118
- Constantin Năstăsescu, Strongly graded rings of finite groups, Comm. Algebra 11 (1983), no. 10, 1033–1071. MR 700723, DOI 10.1080/00927872.1983.10487600
- Declan Quinn, Group-graded rings and duality, Trans. Amer. Math. Soc. 292 (1985), no. 1, 155–167. MR 805958, DOI 10.1090/S0002-9947-1985-0805958-0
- Michel Van den Bergh, A duality theorem for Hopf algebras, Methods in ring theory (Antwerp, 1983) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 129, Reidel, Dordrecht, 1984, pp. 517–522. MR 770615
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 217-221
- MSC: Primary 16A74; Secondary 16A03, 16A08, 16A24, 16A72
- DOI: https://doi.org/10.1090/S0002-9939-1986-0854022-X
- MathSciNet review: 854022