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Transactions of the American Mathematical Society

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



Prime ideals in polycyclic crossed products

Author: D. S. Passman
Journal: Trans. Amer. Math. Soc. 301 (1987), 737-759
MSC: Primary 16A27; Secondary 16A12
MathSciNet review: 882713
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Abstract: In this paper, we describe the prime ideals $ P$ in crossed products $ R \ast G$ with $ R$ a right Noetherian ring and with $ G$ a polycyclic-by-finite group. This is achieved through a series of reductions. To start with, we may assume that $ P \cap R = 0$ so that $ R$ is a $ G$-prime ring. The first step uses a technique of M. Lorenz and the author to reduce to a prime ring and a subgroup of finite index in $ G$. Next if $ R$ is prime, then we show that the prime ideals of $ R \ast G$ disjoint from $ R$ are explicitly determined by the primes of a certain twisted group algebra of a normal subgroup of $ G$. Finally the prime ideals in twisted group algebras of polycyclic-by-finite groups are studied by lifting the situation to ordinary group algebras where the results of J. E. Roseblade can be applied.

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Article copyright: © Copyright 1987 American Mathematical Society