• The Near ring (G,+,*) on a Finite Cyclic Group (G,+) with a function on G

Abstract

Let (G,+,*) be a left near ring on a finite cyclic group (G,+) Let Π be a function defined on G : p * 1 = p for every p ∈ G .This paper describes some theorems: (i) If the left distribution of * over + is also a right distributive over + in (G,+,*) , the function Π on (G,+) is a homomorphism and vice versa. (ii) If the operation * is commutative on (G,+,*) , Π(p).q = p.Π(q) for all p,q ∈ G and vice versa.(iii) If the near ring (G,+,*) is a non-identity integral domain, the function Π is a homomorphism on (G,+,*) such that Π(p.Π(q) )= Π(p).Π(q)≠0 whenever p.q≠ 0 and vice versa.