Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 2, pp. 531-546 (2010)

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Generalized GCD rings. III

Majid M. Ali

Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, P. C. 123 Al-Khod, Sultanate of Oman; e-mail:

Abstract: Greatest common divisors and least common multiples of fractional invertible ideals, finitely generated faithful multiplication ideals and finitley generated projective ideals have been investigated in [A1], [A2] and [A3]. In this paper we extend these results to finitely generated flat ideals. We also study the greatest common divisors and least common multiples of polynomials whose coefficients are invertible ideals, generalizing results concerning GCD domains to GGCD domains.

[A1] Ali, M. M.: Some remarks on generalized GCD domains. Commun. Algebra {\bf 36} (2008), 142--164. [A2] Ali, M. M.; Smith, D. J.: Generalized GCD rings II. Beitr. Algebra Geom. {\bf 44} (2003), 75--98. [A3] Ali, M. M.; Smith, D. J.: Generalized GCD rings. Beitr. Algebra Geom. {\bf 42} (2001), 219--233.

Keywords: greatest common divisor, least common multiple, multiplication ideal, invertible ideal, pure ideal, flat ideal, primitive polynomial

Classification (MSC2000): 13A15, 13F20

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Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.

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