TORSION-FREE, DIVISIBLE, AND MITTAG-LEFFLER MODULES

摘要

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.