### 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 |
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Pages (from-to) | 127-135 |

Number of pages | 9 |

Journal | Periodica Mathematica Hungarica |

Volume | 44 |

Issue number | 2 |

Publication status | Published - 2002 |

### Keywords

- Multiplication ideal
- Multiplication module

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Ali, M. M., & Smith, D. J. (2002). Multiplication modules and a theorem of P. F. Smith.

*Periodica Mathematica Hungarica*,*44*(2), 127-135.