FCG-projective modules and some rings

A module M
R
is called FCG-projective if Ext
R
¹
(M, A) = 0 for every finitely cogenerated right R-module A. A ring R is called right co-hereditary if every factor module of a finitely cogenerated injective right R-module is injective. Some characterizations of FCG-projective modules, right co-hereditary rings and right V-rings are given. FCG-projective dimensions of modules are defined, and FCG-projective dimensions of modules over right co-notherian rings are studied.