Abstract: The Cartan-Eilenberg-Bass Theorem for GV-Noetherian rings is given. The class of weak GV-injective modules is introduced to characterize DW-rings and von Neumann regular rings. In particular, it is proved that the ring is von Neumann regular if and only if any weak GV-injective module is an absolutely pure module, and if and only if any weak GV-injective module is coflat. Finally, the Megibben Theorem for GV-Noetherian rings is obtained. Meanwhile, some examples are provided to distinguish Noetherian rings, GV-Noetherian rings, and w-Noetherian rings.

Key words: GV-Noetherian ring, weak GV-injective module, GV-injective module, DW-ring, von Neumann regular ring