On prime and semiprime near-rings with derivations

Abstract

Let N be a semiprime right near-ring, A a subset of N such that 0∈A and AN⫅A, and d a derivation of N The purpose of this paper is to prove that if d acts as a homomorphism on A or as an anti-homomorphism on A, then d(A)={0}.

Keywords

• prime near-ring
• semiprime near ring
• ideal
• derivation
• homomorphism
• anti-homomorphism.