Flat relative Mittag-Leffler modules and approximations

TL;DR

This paper characterizes flat relative Mittag-Leffler modules through their local structure, confirms Enochs' Conjecture for these classes, and applies findings to f-projective modules, advancing understanding of module approximations.

Contribution

It provides a new characterization of flat relative Mittag-Leffler modules and verifies Enochs' Conjecture for these classes, extending previous work.

Findings

Characterization of flat relative Mittag-Leffler modules via local structure

Verification of Enochs' Conjecture for classes __Q

Application to f-projective modules

Abstract

The classes $\mathcal D _{\mathcal Q}$ of flat relative Mittag-Leffler modules are sandwiched between the class $\mathcal F \mathcal M$ of all flat (absolute) Mittag-Leffler modules, and the class $\mathcal F$ of all flat modules. Building on the works of Angeleri H\" ugel, Herbera, and \v Saroch, 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 $\mathcal D _{\mathcal Q}$. In the final section, we apply these results to the particular setting of f-projective modules.