SKEW GROUP-RINGS AND FREE RINGS

In this paper, we briefly discuss problems posed by S. Montgomery and E. A. Whelan. The first concerns the skew group ring AG. Specifically the problem is to determine when AG is prime in terms of the action of the finite group G on the ring A. Here we are quite far from the answer, but we do exhibit some of the subtleties involved. The second problem is more technical and concerns whether a certain induced module from a primitive ring R to its left Martindale ring of quotients can be zero. In this case we give a positive answer by taking R to be an appropriate free ring. © 1990.