Central Idempotents in Group Rings

Abstract

Let R be a ring and G a group. The group ring RG consists of all functions f: G → R with finite support. Addition is pointwise and multiplication is defined for f, h ∊ RG and g ∊ G, byThe support group of f is defined to be the subgroup of G generated by the support of f. The element f is idempotent if ff = fWe prove the following result.