Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand; e-mail: majid@math.auckland.ac.nz; smith@math.auckland.ac.nz
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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