Abstract
Strongly prime rings were introduced by Handelman and Lawrence [5] and in [2] Groenewald and Heyman investigated the upper radical determined by the class of all strongly prime rings. In this paper we extend the concept of strongly prime to near-rings. We show that the class M of distributively generated near-rings is a special class in the sense of Kaarli [6]. We also show that if N is any distributively generated near-ring, then UM(N), UM denotes the upper radical determined by the class M, coincides with the intersection of all the strongly prime ideals of N.
Publisher
Cambridge University Press (CUP)
Reference11 articles.
1. Special radicals of near-rings (in Russian);Kaarli;Tartu Riikl. Ül. Toimetised Vih.,1982
2. ON THE GROENEWALD-HEYMAN STRONGLY PRIME RADICAL
3. Certain classes of ideals in group rings II
4. 1. Anderson T. , Kaarli K. and Wiegandt R. , Radicals and subdirect decomposition, preprint.
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. P-properties in Near-rings;Journal of Mathematical and Fundamental Sciences;2019-08
2. Topological rings, homogeneous functions, and primeness;Communications in Algebra;2016-10-11
3. Strongly Prime Near-Ring Modules;Arabian Journal for Science and Engineering;2011-08-12
4. Prime radicals in sandwich near-rings;Acta Mathematica Hungarica;2011-02-22
5. Strongly Prime Ideals of Near-rings of Continuous Functions;Advances in Ring Theory;2010