Glasgow Mathematical Journal

Research Article

On the group ring of a free product with amalgamation

Camilla R. Jordana1

a1 c/o Dr. D. A. Jordan, Department of Pure Mathematics, The University of Sheffield, The Hicks Building, Sheffield S3 7RH

Let G = A*HB be the free product of the groups A and B amalgamating the proper subgroup H and let R be a ring with 1. If H is finite and G is not finitely generated we show that any non-zero ideal I of R(G) intersects non-trivially with the group ring R(M), where M = M(I) is a subgroup of G which is a free product amalgamating a finite normal subgroup. This result compares with A. I. Lichtman's results in [6] but is not a direct generalisation of these.

(Received April 02 1979)