Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 117-129, 2019
Gorenstein projective complexes with respect to cotorsion pairs
Renyu Zhao, Pengju Ma
Received April 25, 2017. Published online July 10, 2018.
Abstract: Let $(\mathcal{A,B})$ 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 $(\mathcal{A}, \mathcal{B})$ are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair $(\mathcal{A}, \mathcal{B})$. 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.
Keywords: cotorsion pair; Gorenstein projective complex with respect to cotorsion pairs; stability of Gorenstein categories
Affiliations: Renyu Zhao (corresponding author), Department of Mathematics, Northwest Normal University, Anning East road No. 967, Lanzhou, Gansu, 730070, P. R. China, and Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China, e-mail: zhaory@nwnu.edu.cn; Pengju Ma, Department of Mathematics, Northwest Normal University, Anning East road No. 967, Lanzhou, Gansu, 730070, P. R. China, e-mail: 2642293920@qq.com