Smarandache Idempotents in Finite Ring [Z.Sub.N] and in Group Ring [Z.Sub.N]G‪.‬

Abstract In this paper we analyze and study the Smarandache idempotents (S-idempotents) in the ring [Z.sub.n] and in the group ring [Z.sub.n]G of a finite group G over the finite ring [Z.sub.n]. We have shown the existance of Smarandache idempotents (S-idempotents) in the ring [Z.sub.n] when n = [2.sup.m]p (or 3p), where p is a prime 2 (or p a prime 3). Also we have shown the existance of Smarandache idempotents (S-idempotents) in the group ring [Z.sub.2]G and [Z.sub.2]Sn where n = [2.sup.m]p (p a prime of the form [2.sup.m]t + 1). [section] 1. Introduction