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Proceedings of the American Mathematical Society

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Prime length of crossed products


Author: Charles C. Welsh
Journal: Proc. Amer. Math. Soc. 106 (1989), 91-98
MSC: Primary 16A27; Secondary 20C07
DOI: https://doi.org/10.1090/S0002-9939-1989-0965248-1
MathSciNet review: 965248
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Abstract: In this paper we show that the prime length of a crossed product $ R*G$, where $ R$ is a right Noetherian ring and $ G$ is a polycyclic-by-finite group, is bounded by the plinth length of $ G$ and the prime length of $ R$. We begin by considering prime ideals in group rings of finitely generated Abelian groups, and generalize a theorem of J. E. Roseblade. We then use the description of prime ideals in crossed products given by D. S. Passman to achieve the result.


References [Enhancements On Off] (What's this?)

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  • [2] -, Group rings of polycyclic groups, in Group Theory: Essays for Phillip Hall (K. H. Gruenberg and J. E. Roseblade editors), Academic Press, New York, 1984. MR 780571 (86e:16019)
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  • [5] B. A. F. Wehrfritz, Infinite linear groups, Springer-Verlag, New York, 1973. MR 0335656 (49:436)

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DOI: https://doi.org/10.1090/S0002-9939-1989-0965248-1
Article copyright: © Copyright 1989 American Mathematical Society

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