(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Two generalizations of the completely prime radical of rings to near-rings, namely the completely prime radical of near-rings and the completely equiprime radical of near-rings were introduced and studied. First one is not a Kurosh-Amitsur radical but the second one is a special radical in near-rings. In this article another generalization of the completely prime radical of rings is introduced in near-rings using right modules of near-rings. For this completely prime right N-groups of type-r(1) are introduced in near-rings, N is a near-ring. Making use of these right N-groups of type-r(1), the completely prime radical of near-rings of type-r(1) is introduced. It is observed that the completely prime radical of type-r(1) is a Kurosh-Amitsur radical.