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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Primitive group rings


Authors: Edward Formanek and Robert L. Snider
Journal: Proc. Amer. Math. Soc. 36 (1972), 357-360
MSC: Primary 16A26; Secondary 20C05
MathSciNet review: 0308178
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0308178-8
PII: S 0002-9939(1972)0308178-8
Keywords: Group ring, primitive ring, prime ring
Article copyright: © Copyright 1972 American Mathematical Society