Generalized GCD rings

Majid M. Ali, David J. Smith

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)219-233
Number of pages15
JournalBeitrage zur Algebra und Geometrie
Volume42
Issue number1
Publication statusPublished - 2001

Fingerprint

Faithful
Finitely Generated
Ring
Multiplication
Zero-divisor
Intersection
Generalise

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Ali, M. M., & Smith, D. J. (2001). Generalized GCD rings. Beitrage zur Algebra und Geometrie, 42(1), 219-233.

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

In: Beitrage zur Algebra und Geometrie, Vol. 42, No. 1, 2001, p. 219-233.

Research output: Contribution to journalArticle

Ali, MM & Smith, DJ 2001, 'Generalized GCD rings', Beitrage zur Algebra und Geometrie, vol. 42, no. 1, pp. 219-233.
Ali, Majid M. ; Smith, David J. / Generalized GCD rings. In: Beitrage zur Algebra und Geometrie. 2001 ; Vol. 42, No. 1. pp. 219-233.
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