In this paper we establish the existance of S-idempotents in case of loop rings ZtLn(m) for a special class of loops Ln(m); over the ring of modulo integers Zt for a specific value of t.These loops satisfy the conditions g 2 i = 1 for every gi ∈ Ln(m). We prove ZtLn(m) has an S-idempotent when t is a perfect number or when t is of the form 2p or 3p (where p is an odd prime) or in general when t...