Geodesic
The Coefficient Ring of a Primitive Group Ring
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 489-494

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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 followingTHEOREM 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. 
Lawrence, John. The Coefficient Ring of a Primitive Group Ring. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 489-494. doi: 10.4153/CJM-1975-058-7
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