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Indecomposable modules over Nagata valuation domains

Authors: D. Arnold and M. Dugas
Journal: Proc. Amer. Math. Soc. 122 (1994), 689-696
MSC: Primary 13F30; Secondary 13C05
MathSciNet review: 1239795
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Abstract: For a discrete valuation ring R, let $ {\text{fr}}(R)$ be the supremum of the ranks of indecomposable finite rank torsion-free R-modules. Then $ {\text{fr}}(R) = 1,2,3$, or $ \infty $. A complete list of indecomposables is given if $ {\text{fr}}(R) \leq 3$, in which case R is known to be a Nagata valuation domain.

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Article copyright: © Copyright 1994 American Mathematical Society