Rings with singular modules having a restricted subprojectivity domain

Given modules X and Y, X is said to be Y-subprojective if for every epimorphism pi : P -> Y and every homomorphism a : X -> Y, there exists a homomorphism gamma : X -> P such that pi gamma = a. For a module X, the subprojectivity domain of X is defined to be the collection of all modules Y such that X is Y-subprojective. The class of ec-flat modules is the smallest possible subprojectivity domain of a goldie torsion module. In this paper, we consider goldie torsion modules whose subprojectivty domains contain only ec-flat modules, and we referred to these modules as gb-indigent.We investigate the rings over which every goldie torsion (singular, simple) module is either projective (ec-flat) or gp-indigent. Furthermore, gp-indigent modules on right nonsingular rings are characterized.