Isomorphic Group Rings

Abstract

Let R and S be rings with 1, G a group and RG and SG the corresponding group rings. In this paper, we study the problem of when RG≃SG implies R≃S. This problem was previously investigated in [8] for the case where G is assumed to be infinite cyclic. The corresponding question for polynomial rings, namely, when does R[x]≃S[x] imply R≃S, has been considered by several authors, particularly Coleman and Enochs [3].