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.