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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Isomorphic group rings with nonisomorphic commutative coefficients


Author: Jan Krempa
Journal: Proc. Amer. Math. Soc. 83 (1981), 459-460
MSC: Primary 16A27
MathSciNet review: 627669
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Abstract: Let $ X$ be an infinite cyclic group. An example of two noncommutative nonisomorphic rings $ R$, $ S$ such that their group rings $ RX$, $ SX$ are isomorphic has been given in [1]. In the present note, we show that there also exist commutative nonisomorphic noetherian domains $ A$, $ B$ of Krull dimension 2 such that the group rings $ AX$, $ BX$ are isomorphic. That solves Problem 27 of [4] in the negative.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627669-9
Article copyright: © Copyright 1981 American Mathematical Society