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