Geodesic
Gorenstein projective complexes with respect to cotorsion pairs
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 117-129 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/CMJ.2018.0194-17
Classification : 18G25, 18G35
Keywords: cotorsion pair; Gorenstein projective complex with respect to cotorsion pairs; stability of Gorenstein categories 
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Zhao, Renyu; Ma, Pengju. Gorenstein projective complexes with respect to cotorsion pairs. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 117-129. doi: 10.21136/CMJ.2018.0194-17

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