Singularity Categories with Respect to Ding Projective Modules

作     者：Wen Jing CHEN Zhong Kui LIU Xiao Yan YANG 

作者机构：Department of Mathematics Northwest Normal University Lanzhou 730070 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2017年第33卷第6期

页      面：793-806页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11261050,11361051 and 11361052) Program for New Century Excellent Talents in University(Grant No.NCET-13-0957) 

主　　题：Ding projective module Ding singularity category Ding defect category 

摘      要：Abstract We introduce the singularity category with respect to Ding projective modules, Db dpsg（R）, as the Verdier quotient of Ding derived category Db DP（R） by triangulated subcategory Kb（DP）, and give some triangle equivalences. Assume DP is precovering. We show that Db DP（R） ≌K-,dpb（DP） and Dbpsg（R） ≌ DbDdefect（R）. We prove that each R-module is of finite Ding projective dimension if and only if Dbdpsg（R） = 0.