Flat relative Mittag-Leffler modules and approximations

Abstract

The classes [Formula: see text] of flat relative Mittag-Leffler modules are sandwiched between the class [Formula: see text] of all flat (absolute) Mittag-Leffler modules, and the class [Formula: see text] of all flat modules. Building on the works of Angeleri Hügel, Herbera, and Šaroch, we give a characterization of flat relative Mittag-Leffler modules in terms of their local structure, and show that Enochs’ Conjecture holds for all the classes [Formula: see text]. In the final section, we apply these results to the particular setting of [Formula: see text]-projective modules.