Gorenstein Projective Coresolutions and Co-Tate Homology Functors  

作　　者：Zhongkui Liu Li Wang 

机构地区：[1]Department of Mathematics,Northwest Normal University Lanzhou 730070,Chin

出　　处：《Algebra Colloquium》2023年第1期1-14,共14页代数集刊（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11971388).

摘　　要：For a local commutative Gorenstein ring R,Enochs et al.in[Gorenstein projective resolvents,Comm.Algebra 44(2016)3989-4000)defined a functor Extn^(R)(-,-)and showed that this functor can be computed by taking a totally acyclic complex arising from a projective coresolution of the first component or a totally acyclic complex arising from a projective resolution of the second component.In order to define the functor Extn^(R)(-,-)over general rings,we introduce the right Gorenstein projective dimension of an R-module M,RGpd(M),via Gorenstein projective coresolutions,and give some equivalent characterizations for the finiteness of RGpd(M).Then over a general ring R we define a co-Tate homology group Extn^(R)(-,-) for R-modules M and N with RGpd(M)<oo and Gpd(N)<∞,and prove that Extn^(R)(M,N)can be computed by complete projective coresolutions of the first variable or by complete projective resolutions of the second variable.

关 键 词：Gorenstein projective preenvelope Gorenstein projective coresolution right Gorenstein projective dimension co-Tate homology functor 

分 类 号：O15[理学—数学]