arXiv:1112.0599 Abstract | arXiv Analytics

arXiv:1112.0599 [math.AC]Abstract References Reviews Resources

On completely decomposable and separable modules over Prüfer domains

Published 2011-12-02Version 1

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.

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

DOI: 10.1216/JCA-2010-2-2-159

Categories: math.AC, math.GR

Subjects: 13C13, 13C05, 13F05

Keywords: prüfer domains, separable modules, pontryagin-hill type theorem, separable torsion-free abelian groups, domains summands

Tags: journal article

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