  In this paper we study S-idempotents of the group ring \mathbb{Z}_2G where G
is a finite cyclic group of order n. We give a condition on n such that every
nonzero idempotent element of the group ring \mathbb{Z}_2G is Smarandache
idempotent and we find Smarandache idempotents of the group ring KG, where K is
an algebraically closed field of characteristic 0 and G is a finite cyclic
group.
