Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 1, pp. 219-233 (2001)

Generalized GCD Rings

Majid M. Ali; David J. Smith

Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand; e-mail:;

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.

Keywords: multiplication ideal, Prüfer domain, greatest common divisor, least common multiple

Classification (MSC2000): 13A15; 13F05

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