A Kurosh-Amitsur Completely Prime Radical for Near-rings (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.