FILTERED-PROJECTIVE AND SEMIFLAT MODULES

Abstract

A module P is called F-filtered-projective if for any epimorphism β: B → C and any homomorphism Y: P → C factoring through F, there exists a homomorphism α P → B such that β α = y. We collect for a given module P all such modules F into a class F(P) and all exact sequences relative to which P has the projective property, into a class E(P). Starting with & class P of modules P, we construct the classes F(p) and E(p) as the Intersections of the classes F(P) and E(P) respectively as P runs through P. Relative properties of these classes are investigated and in the special case where P is the class of finitely presented modules, we find a new characterization of flat modules which enables us to introduce the concept of semiflatness which in turn is utilized in a characterization of IF, QF and QF-3 rings.