A kurosh-amitsur prime radical for near-rings

Abstract

The usual definition of primeness for near-rings does not lead to a Kurosh-Amitsur radical class for zerosymmetric near-rings (cf. Kaarli and Kriis[5]). In this paper, we define equiprime near-rings, which are another generalization of primeness in rings. Various results are proved, amongst others, for zerosymmetric near-rings:If N is a near-ring and A ⊲ B ⊲ N such that B/A is equiprime, then A ⊲ N. We define . Then p∗ is a Kurosh-Amitsur radicial for which holds for all ideals I of N. Moreover , where j 3 is the Jacobson-type radical which was introduced by Holcombe, with equality if N has the descending chain condition on N-sub-groups.