Characterization of 3-prime near-rings via multiplicative derivations

Abstract

In this paper, we will prove some theorems concerning the commutativity of a 3-prime near-rings which satisfy some differential identities on semigroup ideals and Jordan ideals of a near-ring \(\mathcal{N}\) admitting a multiplicative derivation. After this, we discuss an example to prove that the necessity of the 3-primeness hypothesis imposed on the various theorems cannot be marginalized.