Abstract :
Let $R$ be a ring, and let $n, d$ be non-negative integers. A right $R$-module $M$ is called $(n, d)$-projective if $Ext^{d+1}_R(M, A)=0$ for every $n$-copresented right $R$-module $A$. $R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted, it is called a right co-$(n,d)$-ring if every right $R$-module is $(n, d)$-projective. $R$ is called right
$n$-cosemihereditary if every submodule of a projective right $R$-module is
$(n, 0)$-projective, it is called a right
$n$-V-ring if it is a right co-$(n,0)$-ring. Some properties of $(n, d)$-projective modules and $(n, d)$-projective dimensions of modules over $n$-cocoherent rings are studied. Certain characterizations of $n$-copresented modules, $(n, 0)$-projective modules, right $n$-cocoherent rings, right $n$-cosemihereditary rings, as well as right $n$-V-rings are given respectively.
