### Abstract

In this article, we study the implication of the primitivity of a matrix near-ring M _{n} (R) (n > 1) and that of the underlying base near-ring R. We show that when R is a zero-symmetric near-ring with identity and M _{n}(R)has the descending chain condition on M _{n}(R)-subgroups, then the 0-primitivity of M _{n}(R)implies the 0-primitivity of R. It is not known if this is true when the descending chain condition on M _{n}(R)is removed. On the other hand, an example is given to show that this is not true in the case of generalized matrix near-rings.

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

Pages (from-to) | 353-363 |

Number of pages | 11 |

Journal | Monatshefte fur Mathematik |

Volume | 165 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2012 Mar 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Monatshefte fur Mathematik*,

*165*(3-4), 353-363. https://doi.org/10.1007/s00605-010-0267-z

}

*Monatshefte fur Mathematik*, vol. 165, no. 3-4, pp. 353-363. https://doi.org/10.1007/s00605-010-0267-z

**Matrix near-rings and 0-primitivity.** / Ke, Wen-Fong; Meyer, J. H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Matrix near-rings and 0-primitivity

AU - Ke, Wen-Fong

AU - Meyer, J. H.

PY - 2012/3/1

Y1 - 2012/3/1

N2 - In this article, we study the implication of the primitivity of a matrix near-ring M n (R) (n > 1) and that of the underlying base near-ring R. We show that when R is a zero-symmetric near-ring with identity and M n(R)has the descending chain condition on M n(R)-subgroups, then the 0-primitivity of M n(R)implies the 0-primitivity of R. It is not known if this is true when the descending chain condition on M n(R)is removed. On the other hand, an example is given to show that this is not true in the case of generalized matrix near-rings.

AB - In this article, we study the implication of the primitivity of a matrix near-ring M n (R) (n > 1) and that of the underlying base near-ring R. We show that when R is a zero-symmetric near-ring with identity and M n(R)has the descending chain condition on M n(R)-subgroups, then the 0-primitivity of M n(R)implies the 0-primitivity of R. It is not known if this is true when the descending chain condition on M n(R)is removed. On the other hand, an example is given to show that this is not true in the case of generalized matrix near-rings.

UR - http://www.scopus.com/inward/record.url?scp=84857648271&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857648271&partnerID=8YFLogxK

U2 - 10.1007/s00605-010-0267-z

DO - 10.1007/s00605-010-0267-z

M3 - Article

VL - 165

SP - 353

EP - 363

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 3-4

ER -