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 in crossed products with a right Noetherian ring and with a polycyclic-by-finite group. This is achieved through a series of reductions. To start with, we may assume that so that is a -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 . Next if is prime, then we show that the prime ideals of disjoint from are explicitly determined by the primes of a certain twisted group algebra of a normal subgroup of . 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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DOI:
http://dx.doi.org/10.1090/S0002-9947-1987-0882713-9

Article copyright:
© Copyright 1987
American Mathematical Society