### 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 I_{3}, 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 |
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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

### Cite this

*Communications in Algebra*,

*18*(9), 3111-3122. https://doi.org/10.1080/00927879008824063