We give a characterization of -cotorsion modules over valuation domains in terms of descending chain conditions on certain chains of definable subgroups. We prove that pure submodules, direct products and modules elementarily equivalent to a -cotorsion module are again -cotorsion. Moreover, we describe the structure of -cotorsion modules.
Sigma-cotorsion modules over valuation domains
BAZZONI, SILVANA;
2009
Abstract
We give a characterization of -cotorsion modules over valuation domains in terms of descending chain conditions on certain chains of definable subgroups. We prove that pure submodules, direct products and modules elementarily equivalent to a -cotorsion module are again -cotorsion. Moreover, we describe the structure of -cotorsion modules.
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