On completely decomposable and separable modules over Prüfer domains

Details On completely decomposable and separable modules over Prüfer domains On completely decomposable and separable modules over Prüfer domains

2011-12-02

arxiv.org/abs/1112.0599v1

Journal of Commutative Algebra 2(2), pp. 159-176, 22 Jun 2010

Mathematics

Commutative Algebra

Scientific paper

10.1216/JCA-2010-2-2-159

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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