### Abstract

All rings are assumed to be commutative with identity. A generalized GCD ring (G-GCD ring) is a ring (zero-divisors admitted) in which the intersection of every two finitely generated (f.g.) faithful multiplication ideals is a f.g. faithful multiplication ideal. Various properties of G-GCD rings are considered. We generalize some of Jäger's and Lüneburg's results to f.g. faithful multiplication ideals.

Original language | English |
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Pages (from-to) | 219-233 |

Number of pages | 15 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 42 |

Issue number | 1 |

Publication status | Published - 2001 |

### Keywords

- Greatest common divisor
- Least common multiple
- Multiplication ideal
- Prüfer domain

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Ali, M. M., & Smith, D. J. (2001). Generalized GCD rings.

*Beitrage zur Algebra und Geometrie*,*42*(1), 219-233.