Infinite crossed products and group-graded rings

Passman, D. S.

doi:10.1090/S0002-9947-1984-0743740-2

Infinite crossed products and group-graded rings
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Trans. Amer. Math. Soc. 284 (1984), 707-727 Request permission

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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