Isomorphic group rings with nonisomorphic commutative coefficients
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- by Jan Krempa PDF
- Proc. Amer. Math. Soc. 83 (1981), 459-460 Request permission
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.References
- L. Grünenfelder and M. M. Parmenter, Isomorphic group rings with nonisomorphic coefficient rings, Canad. Math. Bull. 23 (1980), no. 2, 245–246. MR 576107, DOI 10.4153/CMB-1980-034-4
- Helmut Hasse, Number theory, Akademie-Verlag, Berlin, 1979. Translated from the third German edition of 1969 by Horst Günter Zimmer. MR 544018
- Jan Krempa, Isomorphic group rings of free abelian groups, Canadian J. Math. 34 (1982), no. 1, 8–16. MR 650848, DOI 10.4153/CJM-1982-002-8
- Sudarshan K. Sehgal, Topics in group rings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 50, Marcel Dekker, Inc., New York, 1978. MR 508515
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 459-460
- MSC: Primary 16A27
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627669-9
- MathSciNet review: 627669