Polycyclic group algebras and theorems of Harper and Lichtman (Q914827)

We present an alternative proof of a not so recent theorem of \textit{D. L. Harper} [see Theorem C of Math. Proc. Camb. Philos. Soc. 88, 15-31 (1980; Zbl 0438.16005)] and use it to give an alternative proof of a very recent theorem of \textit{A. I. Lichtman} [see `Trace functions in the ring of fractions of polycyclic group rings' (preprint 1989)]. Harper's theorem concerns the existence of many large semiprime ideals, in the group algebra over a field of a free abelian group A of finite rank, invariant under the action of a polycyclic-by-finite group of automorphisms of A. Lichtman's theorem is that the classical ring of quotients of the group algebra over a field F of a polycyclic-by-finite group is locally super- residually finite-dimensional over F.