On the primitivity of group rings of amalgamated free products
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- by Bola O. Balogun PDF
- Proc. Amer. Math. Soc. 106 (1989), 43-47 Request permission
Abstract:
In this paper we prove the primitivity of the group ring $F[G]$ where $F$ is a field and $G$ belongs to a certain class of free products of groups with amalgamation studied recently by the author. Thus our result generalizes a result of Formanek on free products of groups.References
- Bola O. Balogun, $C^*$-algebras associated with amalgamated products of groups, Glasgow Math. J. 29 (1987), no. 2, 143–148. MR 901660, DOI 10.1017/S0017089500006789
- Edward Formanek, Group rings of free products are primitive, J. Algebra 26 (1973), 508–511. MR 321964, DOI 10.1016/0021-8693(73)90011-2
- Joachim Lambek, Lectures on rings and modules, 2nd ed., Chelsea Publishing Co., New York, 1976. MR 0419493
- Colin M. McGregor, On the primitivity of the group ring of a free group, Bull. London Math. Soc. 8 (1976), no. 3, 294–298. MR 419509, DOI 10.1112/blms/8.3.294
- D. S. Passman, Primitive group rings, Pacific J. Math. 47 (1973), 499–506. MR 332942
- Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 43-47
- MSC: Primary 16A27; Secondary 20C07
- DOI: https://doi.org/10.1090/S0002-9939-1989-0963570-6
- MathSciNet review: 963570