Finiteness Conditions and Relative Singularity Categories  

作　　者：Chun Xia ZHANG 

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第8期1436-1446,共11页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11871125);Natural Science Foundation of Chongqing(Grant No.cstc2021jcyj-msxm X0048)。

摘　　要：We introduce the n-pure projective(resp.,injective)dimension of complexes in n-pure derived categories,and give some criteria for computing these dimensions in terms of the n-pure projective(resp.,injective)resolutions(resp.,coresolutions)and n-pure derived functors.As a consequence,we get some equivalent characterizations for the finiteness of n-pure global dimension of rings.Finally,we study Verdier quotient of bounded n-pure derived category modulo the bounded homotopy category of n-pure projective modules,which is called an n-pure singularity category since it can reflect the finiteness of n-pure global dimension of rings.

关 键 词：n-pure projective dimension n-pure injective dimension n-pure global dimension n-pure derived category n-pure singularity category 

分 类 号：O153.3[理学—数学]