n-Super finitely copresented and n-weak projective modules

Abstract. let r be a ring and n an 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 (wpn (r), wpn (r) ⊥) is a perfect hereditary cotorsion theory and for any n ∈ wpn (r) ⊥, there exists an n-weak projective cover with the unique mapping property if and only if every r-module is n-weak projective