No abstract

Let R be a ring graded by a group G and n ≥ 1 an integer. We introduce the notion of n-FCP-gr-projective R-modules and by using of special finitely copresented graded modules, we investigate that (1) there exist some equivalent characterizations of n-FCP-gr-projective modules and graded right modules of n-FCP-gr-projective dimension at most k over n-gr-cocoherent rings, (2) R is right n-gr-cocoherent if and only if for every short exact sequence 0 → A → B → C → 0 of graded right R-modules, where B and C are n-FCP-gr-projective, it follows that A is n-FCP-gr-projective if and only if (gr-F CPn, gr-F CP ⊥ n ) is a hereditary cotorsion theory, where gr-F CPn denotes the class of n-FCP-gr-projective right modules. Then we examine some of the conditions equivalent to that each right R-module is n-FCP-gr-projective.

No abstract

Let R be a ring graded by a group G and n ≥ 1 an integer. We introduce the notion of n-FCP-gr-projective R-modules and by using of special finitely copresented graded modules, we investigate that (1) there exist some equivalent characterizations of n-FCP-gr-projective modules and graded right modules of n-FCP-gr-projective dimension at most k over n-gr-cocoherent rings, (2) R is right n-gr-cocoherent if and only if for every short exact sequence 0 → A → B → C → 0 of graded right R-modules, where B and C are n-FCP-gr-projective, it follows that A is n-FCP-gr-projective if and only if (gr-F CPn, gr-F CP ⊥ n ) is a hereditary cotorsion theory, where gr-F CPn denotes the class of n-FCP-gr-projective right modules. Then we examine some of the conditions equivalent to that each right R-module is n-FCP-gr-projective.