n-Cotorsion pairs

Motivated by some properties satisfied Gorenstein projective and injective modules over an Iwanaga-Gorenstein ring, we present the concept of left right n-cotorsion pairs in abelian category C. Two classes A B objects C form a pair (A,B) if orthogonality relation ExtCi(A,B)=0 is for indexes 1≤i≤n, every object has resolution whose syzygies have B-resolution dimension at most n−1. This its dual generalise notion complete cotorsion pairs, appealing with approximations, especially those having so called unique mapping property. The main purpose this paper to describe several establish pairs. We also give applications relative homological algebra, that will cover study approximations associated projective, flat chain complexes, as well m-cluster tilting subcategories.