Torsion-free,Divisible, and Mittag-Leffler Modules

We study (relative) 𝒦-Mittag–Leffler modules, with emphasis on the class 𝒦 of absolutely pure modules. A final goal is to describe the 𝒦-Mittag–Leffler abelian groups as those that are, modulo their torsion part, ?₁-free. Several more general results of independent interest are derived on the way. In particular, every flat 𝒦-Mittag–Leffler module (for 𝒦 as before) is Mittag–Leffler. A question about the definable subcategories generated by the divisible modules and the torsion-free modules, resp., has been left open.     

Decidability of the theory of modules over Prüfer domains with dense value groups

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary.