Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 44, No. 1, pp. 75-98 (2003) |
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Generalized GCD Rings IIMajid M. Ali and David J. SmithDepartment of Mathematics, University of Auckland, Auckland, New Zealand; e-mail: majid@math.auckland.ac.nz; e-mail: smith@math.auckland.ac.nzAbstract: 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 Full text of the article:
Electronic version published on: 3 Apr 2003. This page was last modified: 4 May 2006.
© 2003 Heldermann Verlag
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