Let R be a right coherent ring and D^b(R-Mod) the bounded derived category of left R-modules. Denote by D^b(R-Mod)[GF,C] the subcategory of D^b(R-Mod) consisting of all complexes with both finite Gorenstein flat...Let R be a right coherent ring and D^b(R-Mod) the bounded derived category of left R-modules. Denote by D^b(R-Mod)[GF,C] the subcategory of D^b(R-Mod) consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K^b(F∩C) the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D^b(R-Mod)[GF,C]/K^b(F∩C,) is triangle-equivalent to the stable category GF∩C of the Frobenius category of all Gorenstein fiat and cotorsion left R-modules.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11601433 and 11261050)the Postdoctoral Science Foundation of China(Grant No.2106M602945XB)Northwest Normal University(Grant No.NWNU-LKQN-15-12)
文摘Let R be a right coherent ring and D^b(R-Mod) the bounded derived category of left R-modules. Denote by D^b(R-Mod)[GF,C] the subcategory of D^b(R-Mod) consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K^b(F∩C) the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D^b(R-Mod)[GF,C]/K^b(F∩C,) is triangle-equivalent to the stable category GF∩C of the Frobenius category of all Gorenstein fiat and cotorsion left R-modules.