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 language | English |
|---|---|
| Pages (from-to) | 3111-3122 |
| Number of pages | 12 |
| Journal | Communications in Algebra |
| Volume | 18 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - Jan 1 1990 |
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ASJC Scopus subject areas
- Algebra and Number Theory
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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 journal › Article
}
TY - JOUR
T1 - A kurosh-amitsur prime radical for near-rings
AU - Booth, G. L.
AU - Groenewald, N. J.
AU - Veldsman, S.
PY - 1990/1/1
Y1 - 1990/1/1
N2 - 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.
AB - 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.
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U2 - 10.1080/00927879008824063
DO - 10.1080/00927879008824063
M3 - Article
AN - SCOPUS:0012100444
VL - 18
SP - 3111
EP - 3122
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 9
ER -