On completely decomposable and separable modules over Pr\"ufer domains
Commutative Algebra
2011-12-06 v1 Group Theory
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.
Cite
@article{arxiv.1112.0599,
title = {On completely decomposable and separable modules over Pr\"ufer domains},
author = {L. Fuchs and J. E. Macías-Díaz},
journal= {arXiv preprint arXiv:1112.0599},
year = {2011}
}