Abstract
Let R be a valuation domain; an R-module is said to be pathological if it does not contain nonzero uniserial pure submodules. It is shown that there are no pathological R-modules if and only if R is a totally branched, discrete valuation domain. Three characterizations of these domains are given: JR J is principal for all J ε Spec( R); every ideal is isomorphic to a prime ideal; the value group of R is discrete, and the set of convex subgroups is well ordered by inclusion.
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