Relative singularity categories with respect to gorenstein flat modules |
| |
Authors: | Zhen Xing Di Zhong Kui Liu Xiao Xiang Zhang |
| |
Institution: | 1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China;2. Department of Mathematics, Southeast University, Nanjing 210096, P. R. China |
| |
Abstract: | Let R be a right coherent ring and D b (R-Mod) the bounded derived category of left R-modules. Denote by \({D^b}{\left( {R - Mod} \right)_{\widehat {\left {GF,C} \right]}}}\) 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 \({D^b}{\left( {R - Mod} \right)_{\widehat {\left {GF,C} \right]}}}\)/K b (F ∩ C) is triangle-equivalent to the stable category GF ∩ C of the Frobenius category of all Gorenstein flat and cotorsion left R-modules. |
| |
Keywords: | Triangle equivalence Gorenstein flat dimension cotorsion dimension stable category derived category homotopy category |
本文献已被 CNKI SpringerLink 等数据库收录! |
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学学报(英文版)》下载免费的PDF全文 |