Gorenstein projective complexes with respect to cotorsion pairs

Abstract

Let $(\mathcal{A},\mathcal{B})$ be a complete and hereditary cotorsion pair in the category of left $R$-modules. In this paper, the so-called Gorenstein projective complexes respect to the cotorsion pair $(\mathcal{A},\mathcal{B})$ are introduced. We show that these complexes are just the complexes of Gorenstein projective modules respect to the cotorsion pair $(\mathcal{A},\mathcal{B})$. As applications, we prove that both Gorenstein projective modules with respect to cotorsion pairs and Gorenstein projective complexes with respect to cotorsion pairs possess of stability.