Finitely generated projective modules and TTF classes

Abstract

Let P be a finitely generated projective right -module w ith trace ideal T and A -endomorphism ring B. Associated with P are the TTF classes, 2 F = { A X \ P <g) X = 0} and 3 = {X A I Hom(F, X) = 0}. An investigation of these TTF classes yields characterizations of various conditions on P and ; e.g., (1) B P is projective (flat) and (2) A T is projective (flat). The concept of weak stability for a hereditary torsion class is introduced and characterizations are given.