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The Coefficient Ring of a Primitive Group Ring

Published online by Cambridge University Press:  20 November 2018

John Lawrence
John Lawrence*
Affiliation:
McGill University, Montreal, Quebec; Carleton University, Ottawa, Ontario
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All rings are associative with unity. A ring R is prime if xRy ≠ 0 whenever x and y are nonzero. A ring R is (left) primitive if there exists a faithful irreducible left R-module.

If the group ring R[G] is primitive, what can we say about R? First, since every primitive ring is prime, we know that R is prime, by the following

THEOREM 1 (Connell [1, 675]). The group ring R[G] is prime if and only if R is prime and G has no non-trivial finite normal subgroup.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 489 - 494
Copyright
Copyright © Canadian Mathematical Society 1975

References

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