### 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 |
---|---|

Pages (from-to) | 219-233 |

Number of pages | 15 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 42 |

Issue number | 1 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Beitrage zur Algebra und Geometrie*,

*42*(1), 219-233.

**Generalized GCD rings.** / Ali, Majid M.; Smith, David J.

Research output: Contribution to journal › Article

*Beitrage zur Algebra und Geometrie*, vol. 42, no. 1, pp. 219-233.

}

TY - JOUR

T1 - Generalized GCD rings

AU - Ali, Majid M.

AU - Smith, David J.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Greatest common divisor

KW - Least common multiple

KW - Multiplication ideal

KW - Prüfer domain

UR - http://www.scopus.com/inward/record.url?scp=27844493031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27844493031&partnerID=8YFLogxK

M3 - Article

VL - 42

SP - 219

EP - 233

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

IS - 1

ER -