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.
KeywordsNumber Theory Algebraic Geometry Topological Group Integral Domain Finite Conductor
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