Geodesic
Isomorphic Group Rings with Non-Isomorphic Coefficient Rings*
Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 245-246

Voir la notice de l'article provenant de la source Cambridge University Press

The following question has been floating around for some time now and is also stated as Research Problem 26 in [4]:Let R, S be unital rings and let 〈x〉 be an infinite cyclic group. Does R〈x〉≃S〈x〉 imply R≃S?In this note, we present a collection of examples which answer the question in the negative. However, all of these examples consist of non-commutative rings, and the problem is still open in the case where R and S are assumed to be commutative. 
Grünenfelder, L.; Parmenter, M. M. Isomorphic Group Rings with Non-Isomorphic Coefficient Rings*. Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 245-246. doi: 10.4153/CMB-1980-034-4
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