ملخص
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 [formula omitted]. Then P* is a Kurosh-Amitsur radical for which [formula omitted] holds for all ideals I of N. Moreover, [formula omitted], where I3, is the Jacobson-type radical which was introduced by Holcombe, with equality if N has the descending chain condition on N-sub-groups.
اللغة الأصلية | English |
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الصفحات (من إلى) | 3111-3122 |
عدد الصفحات | 12 |
دورية | Communications in Algebra |
مستوى الصوت | 18 |
رقم الإصدار | 9 |
المعرِّفات الرقمية للأشياء | |
حالة النشر | Published - يناير 1 1990 |
منشور خارجيًا | نعم |
ASJC Scopus subject areas
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