Abstract: As a proper generalization of C3 modules, the concept of generalized C3 modules (briefly G-C3 modules) is introduced in this paper. Basic properties of these modules are studied and it is shown that a hereditary ring R is a right V-ring if and only if every finitely cogenerated R-module is a G-C3 module if and only if every finitely copresented R-module is a G-C3 module.

Key words: C3 module, G-C3 module, V-ring