Abstract
If G is a polycyclic group and p is a prime ideal of the group ring Z G, how big is p? For example, is it determined by a relatively small subgroup of G? How long can a chain of prime ideals of Z G be? These are the sort of questions we consider in this chapter. The proofs frequently use induction on the Hirsch number, so we begin by looking at the connection between the prime ideals of Z G and the prime ideals of Z H for H a normal subgroup of G.
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