Smarandache Idempotents in finite ring Z sub( n) and in Group Ring Z sub( n)G

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 super( 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)S sub( n) where n = 2 super( m)p (p a prime of the form 2 super( m)t + 1).