On the group ring of a free product with amalgamation

Jordan, Camilla R. (1980). On the group ring of a free product with amalgamation. Glasgow Mathematical Journal, 21 pp. 135–138.

DOI: https://doi.org/10.1017/S0017089500004092

Abstract

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.

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