Geodesic
On Group Rings
Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 249-254

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Let R be a commutative ring with unity and let G be a group. The group ring RG is a free R-module having the elements of G as a basis, with multiplication induced by The first theorem in this paper deals with idempotents in RG and improves a result of Connell. In the second section we consider the Jacobson radical of RG, and we prove a theorem about a class of algebras that includes RG when G is locally finite and R is an algebraically closed field of characteristic zero. The last theorem shows that if R is a field and G is a finite nilpotent group, then RG determines RP for every Sylow subgroup P of G, regardless of the characteristic of R. 
Coleman, D. B. On Group Rings. Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 249-254. doi: 10.4153/CJM-1970-032-3
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