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arXiv · 1112.0599

On completely decomposable and separable modules over Pr\"ufer domains

L. Fuchs·J. E. Macías-Díaz
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Abstract

We generalize known results on summands of completely decomposable and separable torsion-free abelian groups to modules over h-local Pr\"ufer domains. Over such domains summands of completely decomposable torsion-free modules are again completely decomposable (Theorem 3.2) and summands of separable torsion-free modules are likewise separable (Theorem 4.2). In addition, a Pontryagin-Hill type theorem is established on countable chains of homogeneous completely decomposable modules over h-local Pr\"ufer domains.

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L. Fuchs, J. E. Macías-Díaz. 2011-12-02. On completely decomposable and separable modules over Pr\"ufer domains. https://doi.org/10.1216/jca-2010-2-2-159

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