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Gorenstein Projective Coresolutions and Co-Tate Homology Functors
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作者 Zhongkui Liu Li Wang 《Algebra Colloquium》 SCIE CSCD 2023年第1期1-14,共14页
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... 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. 展开更多
关键词 Gorenstein projective preenvelope Gorenstein projective coresolution right Gorenstein projective dimension co-Tate homology functor
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