The Jacobson radical of the group ring of a generalised free product

A well known problem in group rings asks whether the Jacobson radical is always a nil ideal [9; Problem 15, page 132]. This has been answered in the affirmative for a number of special cases where either the ring or the group is restricted; see, for example, [3], [10]. In particular Formanek has recently shown that group rings of free products are primitive [1]. In this paper we consider the case where the group is a free product with amalgamation. We obtain two main results