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

Jordan, Camilla (1975). The Jacobson radical of the group ring of a generalised free product. Journal of the London Mathematical Society, 2(11) pp. 369–376.

DOI: https://doi.org/10.1112/jlms/s2-11.3.369

Abstract

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.

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