### Abstract

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith's theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules.

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

Pages (from-to) | 127-135 |

Number of pages | 9 |

Journal | Periodica Mathematica Hungarica |

Volume | 44 |

Issue number | 2 |

Publication status | Published - 2002 |

### Fingerprint

### Keywords

- Multiplication ideal
- Multiplication module

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Periodica Mathematica Hungarica*,

*44*(2), 127-135.

**Multiplication modules and a theorem of P. F. Smith.** / Ali, Majid M.; Smith, David J.

Research output: Contribution to journal › Article

*Periodica Mathematica Hungarica*, vol. 44, no. 2, pp. 127-135.

}

TY - JOUR

T1 - Multiplication modules and a theorem of P. F. Smith

AU - Ali, Majid M.

AU - Smith, David J.

PY - 2002

Y1 - 2002

N2 - P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith's theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules.

AB - P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith's theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules.

KW - Multiplication ideal

KW - Multiplication module

UR - http://www.scopus.com/inward/record.url?scp=52649117592&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52649117592&partnerID=8YFLogxK

M3 - Article

VL - 44

SP - 127

EP - 135

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

SN - 0031-5303

IS - 2

ER -