### Abstract

It is shown that in the variety of all, not necessarily 0-symmetric near-rings, there are no non-trivial classes of near-rings which satisfy condition (F), no non-trivial (Kurosh-Amitsur) radical classes with the ADS-property and consequently no non-trivial ideal-hereditary radical classes. It is also shown that any hereditary semisimple class contains only 0-symmetric near-rings.

Original language | English |
---|---|

Pages (from-to) | 185-189 |

Number of pages | 5 |

Journal | Algebra Universalis |

Volume | 36 |

Issue number | 2 |

Publication status | Published - 1996 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Algebra Universalis*,

*36*(2), 185-189.

**The general radical theory of near-rings - Answers to some open problems.** / Veldsman, S.

Research output: Contribution to journal › Article

*Algebra Universalis*, vol. 36, no. 2, pp. 185-189.

}

TY - JOUR

T1 - The general radical theory of near-rings - Answers to some open problems

AU - Veldsman, S.

PY - 1996

Y1 - 1996

N2 - It is shown that in the variety of all, not necessarily 0-symmetric near-rings, there are no non-trivial classes of near-rings which satisfy condition (F), no non-trivial (Kurosh-Amitsur) radical classes with the ADS-property and consequently no non-trivial ideal-hereditary radical classes. It is also shown that any hereditary semisimple class contains only 0-symmetric near-rings.

AB - It is shown that in the variety of all, not necessarily 0-symmetric near-rings, there are no non-trivial classes of near-rings which satisfy condition (F), no non-trivial (Kurosh-Amitsur) radical classes with the ADS-property and consequently no non-trivial ideal-hereditary radical classes. It is also shown that any hereditary semisimple class contains only 0-symmetric near-rings.

UR - http://www.scopus.com/inward/record.url?scp=0038877957&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038877957&partnerID=8YFLogxK

M3 - Article

VL - 36

SP - 185

EP - 189

JO - Algebra Universalis

JF - Algebra Universalis

SN - 0002-5240

IS - 2

ER -