Examples of clean commutative group rings

A ring R is said to be clean if each element of R   can be written as the sum of a unit and an idempotent. In this article we give examples of clean commutative group rings. In particular, we characterize when the group ring Z(p)[Cn]Z(p)[Cn] is clean. The notion of a group ring being clean locally is defined, and it is investigated when the commutative group ring Z(p)[Cn]Z(p)[Cn] is clean locally. It is proved that when R   is a commutative Hensel ring, the commutative group ring R[G]R[G] is clean if and only if G is torsion.