Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 1, pp. 75-98 (2003)
Generalized GCD Rings II
Majid M. Ali and David J. SmithDepartment of Mathematics, University of Auckland, Auckland, New Zealand; e-mail: firstname.lastname@example.org; e-mail: email@example.com
Abstract: Greatest common divisors and least common multiples of quotients of elements of integral domains have been investigated by Lüneburg and further by Jäger. In this paper we extend these results to invertible fractional ideals. We also lift our earlier study of the greatest common divisor and least common multiple of finitely generated faithful multiplication ideals to finitely generated projective ideals.
Keywords: greatest common divisor, least common multiple, invertible ideal, projective ideal, multiplication ideal, flat ideal, Prüfer domain, semihereditary ring, Bezout domain, p.p. ring
Classification (MSC2000): 13A15; 13F05
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Electronic version published on: 3 Apr 2003. This page was last modified: 4 May 2006.