Bulletin of the
Korean Mathematical Society BKMS

Let $(\mathcal{L}, \mathcal{A})$ be a complete duality pair. We give some equivalent characterizations of Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules and construct some model structures and recollements associated to them.

Keywords: Duality pair, Frobenius pair, model structure, recollement

MSC numbers: 16E05, 18G25, 18G80

Supported by: The authors sincerely thank the referee for the helpful suggestions and valuable comments. This work was supported by National Natural Science Foundation of China (Nos. 11761060, 11901463), Science and Technology Project of Gansu Province (20JR5RA517), Innovation Ability Enhancement Project of Gansu Higher Education Institutions (2019A-002) and Improvement of Young Teachers' Scientific Research Ability (NWNU-LKQN-18-30).