Relative Singularity Categories with Respect to Gorenstein Flat Modules

被引：3
|
作者：
Di, Zhen Xing [1 ]
Liu, Zhong Kui [1 ]
Zhang, Xiao Xiang [2 ]
机构：
[1] Northwest Normal Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China
[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2017年 / 33卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Triangle equivalence; Gorenstein flat dimension; cotorsion dimension; stable category; derived category; homotopy category; PROJECTIVE-MODULES; MODEL STRUCTURE; COMPLEXES; DIMENSION; RINGS;
D O I：
10.1007/s10114-017-6566-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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)(left perpendicular (GF,C) over cap right perpendicular) the subcategory of D-b (R-Mod) consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K-b (F boolean AND C) the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D-b (R-Mod)([(GF,C]) over cap) / K-b (F boolean AND C) is triangle-equivalent to the stable category (GF boolean AND C) under bar of the Frobenius category of all Gorenstein flat and cotorsion left R-modules.
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页码：1463 / 1476
页数：14
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