This research introduces a new generalization of the completely prime radical in near-rings, suggesting its connection to Kurosh-Amitsur radicals.
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.
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Lakshminarayana et al. (2025) studied this question.
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