(n,d)-COCOHERENT RINGS, ( n , d ) (n,d)-COSEMIHEREDITARY RINGS an‎d ( n , d ) (n,d)- V V-RINGS

Let R be a ring, n be an non-negative integer and d be a positive integer or ∞. A right R-module M is called (n, d) ∗-projective if Ext1 R(M, C) = 0 for every n-copresented right R-module C of injective dimension ≤ d; a ring R is called right (n, d)-cocoherent if every n-copresented right R-module C with id(C) ≤ d is (n+1)-copresented; a ring R is called right (n, d)-cosemihereditary if whenever 0 → C → E → A → 0 is exact, where C is n-copresented with id(C) ≤ d, E is finitely cogenerated injective, then A is injective; a ring R is called right (n, d)-V -ring if every n-copresented right R-module C with id(C) ≤ d is injective. Some characterizations of (n, d) ∗-projective modules are given, right (n, d)-cocoherent rings, right (n, d)-cosemihereditary rings and right (n, d)-V -rings are characterized by (n, d) ∗-projective right R-modules. (n, d) ∗-projective dimensions of modules over right (n, d)-cocoherent rings are investigated.