n-Super finitely copresented and n-weak projective modules

Let R be a  ring and n a non-negative integer. In this paper,  we first introduce the concept of n-super finitely copresented  R-modules and via these modules, we give a concept of n-weak projective modules and investigate some characterizations of these modules over any arbitrary ring. For example, we obtain that (\mathcal{WP}^{n}(R), \mathcal{WP}^{n}(R)^{\bot}) is a perfect hereditary cotorsion theory and for any N\in \mathcal{WP}^n(R)^{\bot}, there exists an n-weak projective cover with the unique mapping property if and only if every R-module is  n-weak projective.

کلیدواژه ها:

n-weak ‎projective‎ ‎module ، ‎ n-weak ‎inje‎ctive‎ ‎module ، ‎ n-‎super‎ ‎f‎initely‎‎‎ ‎copresented‎ ‎module‎ ، n-super finitely presented