Sigma-cotorsion modules over valuation domains

Abstract

We give a characterization of Sigma-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 Sigma-cotorsion module are again Sigma-cotorsion.

Moreover, we describe the structure of Sigma-cotorsion modules.

Keywords

• Sigma-cotorsion
• modules
• valuation
• domains