A generalization of injective modules (noted GI-modules), distinct from p-injective modules, is introduced. Rings whose p-injective modules are GI are characterized. If M is a left GI-module, E = End ( AM ), then E / J ( E ) is von Neumann regular, where J ( E ) is the Jacobson radical of the ring E . A is semi-simple Artinian if, and only if, every left A -module is GI. If A is a left p. p., left GI-ring such that every non-zero complement left ideal of A contains a non-zero ideal of A , then A is strongly regular. Sufficient conditions are given for a ring to be either von Neumann regular or quasi-Frobenius. Quasi-Frobenius and von Neumann regular rings are characterized. Kasch rings are also considered.