Given a semiprime Goldie module M projective in σ[M ] we study decompositions on its M -injective hull M in terms of the minimal prime in M submodules. With this, we characterize the semiprime Goldie modules in Z-Mod and make a decomposition of the endomorphism ring of M . Also, we investigate the relations among semiprime Goldie modules, QI-modules and co-semisimple modules extending results on left QI-rings and V -rings.