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On finite conductor domains

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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.

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References

  1. CHASE, S. U.: Direct products of modules. Trans. Amer. Math. Soc. 97, 457–493 (1960).

    Google Scholar 

  2. COHN, P. M.: Bezout rings and their subrings. Proc. Cambridge Phil. Soc. 64, 251–264 (1968).

    Google Scholar 

  3. COSTA, D., J. L. MOTT and M. ZAFRULLAH: The The construction D + XDS [X], (to appear).

  4. DOBBS, D.: On going down for simple overrings. Proc. Amer. Math. Soc. 39, 515–519 (1973).

    Google Scholar 

  5. GILMER, R. W.: Multiplicative Ideal Theory. Marcel Dekker, Inc. New York (1972).

    Google Scholar 

  6. GRIFFIN, M.: Some results on v-multiplication rings. Canad. J. Math. 19, 710–722 (1977).

    Google Scholar 

  7. KAPLANSKY, I.: Commutative Rings. Allyn and Bacon, Boston (1970).

    Google Scholar 

  8. McADAM, S.: Two conductor theorems. J. of Alg. 23, 239–240 (1972).

    Google Scholar 

  9. PAPICK, I.: Local minimal overrings. Can. J. Math. 28, 788–792 (1976).

    Google Scholar 

  10. TANG, H. T.: Gauss' Lemma. Proc. Amer. Math. Soc. 35, 372–376 (1972).

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Education at Sebha, Al-Faateh University, P.O.Box 18758, Sebha, Libyan Arab Jamahiriya

    Muhammad Zafrullah

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  1. Muhammad Zafrullah
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Zafrullah, M. On finite conductor domains. Manuscripta Math 24, 191–204 (1978). https://doi.org/10.1007/BF01310053

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  • DOI: https://doi.org/10.1007/BF01310053

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