Primitive group rings
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- by Edward Formanek and Robert L. Snider PDF
- Proc. Amer. Math. Soc. 36 (1972), 357-360 Request permission
Abstract:
Two theorems showing the existence of primitive group rings are proved. Theorem 1. Let G be a countable locally finite group and F a field of characteristic 0, or characteristic p if G has no elements of order p. Then the group ring $F[G]$ is primitive if and only if G has no finite normal subgroups. Theorem 2. Let G be any group, and F a field. Then there is a group H containing G such that $F[H]$ is a primitive ring.References
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- Alan Rosenberg, On the primitivity of the group algebra, Canadian J. Math. 23 (1971), 536–540. MR 286836, DOI 10.4153/CJM-1971-057-8
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 357-360
- MSC: Primary 16A26; Secondary 20C05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0308178-8
- MathSciNet review: 0308178