Special elements in S-rings - abstract

Study of Smarandache Rings (S-rings) started in the year 2002. A S-ring is ring but all rings are not S-rings. We introduce in this paper the notions of Smarandache nilpotent elements, S-semi idempotents, S-pseudo commutative pair and based on these definitions we define new class of S-rings like S-pseudo
commutative rings, S-strongly regular rings and S-quasi commutative rings.