Abstract
An integral domain D is a FC domain if for all a, b in D, aD∩bD is finitely generated. Using a set of very general and useful lemmas, we show that an integrally closed FC domain is a Prüfer v-multiplication domain (PVMD). We use this result to improve some results which were originally proved for integrally closed FC domains (or for coherent domains) to results on PVMD's. Finally we provide examples of integrally closed integral domains which are not FC domains.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
CHASE, S. U.: Direct products of modules. Trans. Amer. Math. Soc. 97, 457–493 (1960).
COHN, P. M.: Bezout rings and their subrings. Proc. Cambridge Phil. Soc. 64, 251–264 (1968).
COSTA, D., J. L. MOTT and M. ZAFRULLAH: The The construction D + XDS [X], (to appear).
DOBBS, D.: On going down for simple overrings. Proc. Amer. Math. Soc. 39, 515–519 (1973).
GILMER, R. W.: Multiplicative Ideal Theory. Marcel Dekker, Inc. New York (1972).
GRIFFIN, M.: Some results on v-multiplication rings. Canad. J. Math. 19, 710–722 (1977).
KAPLANSKY, I.: Commutative Rings. Allyn and Bacon, Boston (1970).
McADAM, S.: Two conductor theorems. J. of Alg. 23, 239–240 (1972).
PAPICK, I.: Local minimal overrings. Can. J. Math. 28, 788–792 (1976).
TANG, H. T.: Gauss' Lemma. Proc. Amer. Math. Soc. 35, 372–376 (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zafrullah, M. On finite conductor domains. Manuscripta Math 24, 191–204 (1978). https://doi.org/10.1007/BF01310053
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01310053