A kurosh-amitsur prime radical for near-rings

G. L. Booth*, N. J. Groenewald, S. Veldsman

*Corresponding author for this work

Research output: Contribution to journalArticle

38 Citations (Scopus)

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 [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.

Original languageEnglish
Pages (from-to)3111-3122
Number of pages12
JournalCommunications in Algebra
Volume18
Issue number9
DOIs
Publication statusPublished - Jan 1 1990

ASJC Scopus subject areas

  • Algebra and Number Theory

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