Transactions of the American Mathematical Society

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



Infinite crossed products and group-graded rings

Author: D. S. Passman
Journal: Trans. Amer. Math. Soc. 284 (1984), 707-727
MSC: Primary 16A27; Secondary 16A03, 20C07
MathSciNet review: 743740
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Abstract: In this paper, we precisely determine when a crossed product $ R\;\ast\;G$ is semiprime or prime. Indeed we show that these conditions ultimately depend upon the analogous conditions for the crossed products $ R\;\ast\;N$ of the finite subgroups $ N$ of $ G$ and upon the interrelationship between the normalizers of these subgroups and the ideal structure of $ R$. The proof offered here is combinatorial in nature, using the $ \Delta $-methods, and is entirely self-contained. Furthermore, since the argument applies equally well to strongly $ G$-graded rings, we have opted to work in this more general context.

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Article copyright: © Copyright 1984 American Mathematical Society