Generalized GCD rings

Majid M. Ali, David J. Smith

Research output: Contribution to journalArticle

5 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2001


  • 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.