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 \(\pi :P\rightarrow Y\) $\pi :P\to Y$ and every homomorphism \(\alpha : X\rightarrow Y\) $\alpha :X\to Y$ , there exists a homomorphism \(\gamma :X\rightarrow P\) $\gamma :X\to P$ such that \(\pi \gamma =\alpha\) $\pi \gamma =\alpha$ . 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.