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

Let R be a ring. A right R-module is said to C-flat if the kernel of any epimorphism B → C-pure in B, i.e. induced map Hom(C,B) Hom(C,A) surjective for cyclic C. Projective modules are and weakly-flat neat-flat. In this article, it discussed connections between C-flat, weakly-flat, neat-flat singly flat modules. It shown that coincide with singly-projective over arbitrary rings. Next, several c...