On finite conductor domains

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1978 Germany English Publisher:Springer Science and Business Media LLCJournal:Manuscripta Mathematica, volume 24, pages 191-204 (issn: 0025-2611, eissn: 1432-1785,

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Authors: Zafrullah, Muhammad;

doi: 10.1007/bf01310053

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 Prufer 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.

Country

Germany

Related Organizations

DigiZeitschriften
Germany

Keywords

510.mathematics, Integral domains, Commutative rings and modules of finite generation or presentation; number of generators, Ideals and multiplicative ideal theory in commutative rings, Article, Dedekind, Prüfer, Krull and Mori rings and their generalizations

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