Torsion-free, divisible, and Mittag-Leffler modules

TL;DR

This paper investigates K-Mittag-Leffler modules, especially over absolutely pure modules, characterizing certain abelian groups and establishing new results on flat modules and definable subcategories.

Contribution

It provides a characterization of K-Mittag-Leffler abelian groups and proves that flat K-Mittag-Leffler modules are Mittag-Leffler, advancing understanding of module classes.

Findings

Characterization of K-Mittag-Leffler abelian groups as torsion-free parts of certain groups

Proof that flat K-Mittag-Leffler modules are Mittag-Leffler

Derived general results on module classes and open questions on definable subcategories

Abstract

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, aleph_1-free, Cor.6.12. 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, Thm.3.9. A question about the definable subcategories generated by the divisible modules and the torsion-free modules, resp., has been left open, Quest.4.6.