Gorenstein projective complexes with respect to cotorsion pairs

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 respect to the cotorsion pair (A, B) are introduced. We show that these complexes are just the complexes of Gorenstein projective modules respect to the cotorsion pair (A, 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.Keywords: cotorsion pair, Gorenstein projective complex with respect to cotorsion pairs, stability. MSC 2010: 18G25, 18G35This result unifies and generalizes of [10, Theorems 4.7] and [18, Theorems 2.2, 3.1]. By this connection, we prove the following results (see Theorem 4.1 and Theorem 4.2, respectively). Theorem 1.2. A left R-module M belongs to G(A) if and only if there exists a Hom R (−, A ∩ B)-exact exact sequence · · ·

Strongly Gorenstein injective complexes with respect to a cotorsion pair

“…As a generalization of projective, injective and flat complexes, Enochs et al introduced Gorenstein projective, injective and flat complexes, and developed Gorenstein homological algebra in the category of complexes in [2]. Renyu Zhao and Pengju Ma introduced Gorenstein projective complexes with respect to a cotorsion pair, that is Gorenstein -projective complexes in [5], and investigate stability of Gorenstein -projective complexes. Definition 1.…”