Abstract
In this paper we analyze and study the Smarandache idempotents (S-idempotents) in the ring of integers modulo n, Z_n. We have shown in general that an idempotent element in a ring R may not be an S-idempotent. Also, we have established the existence of S-idempotents in Z_n for a specific value n. We have proved that Z_nhas an S-idempotents with n is a perfect number, and n is of the form (where p be an odd prime), or ( p a prime greater than 3), or in general when ( and are distinct odd primes). We provide many interesting properties and illustrate them with several examples.