n-Copure projective modules

Let R be a ring, n a fixed nonnegative integer and F (n) the class of all left R-modules of flat dimension at most n. A left R-module M is called n-copure projective if Ext (R) (1) (M,F) = 0 for any F a F (n) . Some examples are given to show that n-copure projective modules need not be m-copure projective whenever m > n. Then we characterize the well-known QF rings and IF rings in terms of n-copure projective modules. Finally, we prove that a ring R is relative left hereditary if and only if every submodule of a projective (or free) left R-module is n-copure projective if and only if id (R) (N) a parts per thousand currency sign 1 for every left R-module N with N a F (n) .