A kurosh-amitsur prime radical for near-rings

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

Research output: Contribution to journalArticle

35 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

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Prime Radical
Near-ring
Chain Condition
Equality
Subgroup
Ring

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Booth, G. L., Groenewald, N. J., & Veldsman, S. (1990). A kurosh-amitsur prime radical for near-rings. Communications in Algebra, 18(9), 3111-3122. https://doi.org/10.1080/00927879008824063

A kurosh-amitsur prime radical for near-rings. / Booth, G. L.; Groenewald, N. J.; Veldsman, S.

In: Communications in Algebra, Vol. 18, No. 9, 01.01.1990, p. 3111-3122.

Research output: Contribution to journalArticle

Booth, GL, Groenewald, NJ & Veldsman, S 1990, 'A kurosh-amitsur prime radical for near-rings', Communications in Algebra, vol. 18, no. 9, pp. 3111-3122. https://doi.org/10.1080/00927879008824063
Booth, G. L. ; Groenewald, N. J. ; Veldsman, S. / A kurosh-amitsur prime radical for near-rings. In: Communications in Algebra. 1990 ; Vol. 18, No. 9. pp. 3111-3122.
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