Abstract
Let R be a noetherian domain of Krull dimension 1. A completely decomposable module is a direct sum of rank one modules, and a Butler module is any torsion-free image of a finite rank, completely decomposable module. Butler modules are closed under quasi-isomorphism. We characterize when the class of Butler modules is closed under the formation of pure submodules. Additionally, when R is analytically unramified, we show that the Butler modules coincide with the class of pure submodules of finite rank completely decomposable modules if and only if for each maximal ideal P of R, there is a unique maximal ideal in the integral closure of R lying over P.
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Goeters, H.P. (1999). Butler modules over 1-dimensional Noetherian domains. In: Eklof, P.C., Göbel, R. (eds) Abelian Groups and Modules. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7591-2_12
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DOI: https://doi.org/10.1007/978-3-0348-7591-2_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7593-6
Online ISBN: 978-3-0348-7591-2
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