Polycyclic Group Rings Whose Principal Ideals Are Projective

Let K[G] be a prime group algebra with G a polycyclic-by-finite group. In this paper we prove that K[G] is a CS-ring or a PP-ring if and only if either G is torsion-free or G D∞ and char K ≤ 2. The proof requires group theoretic as well as group ring arguments.