首页|Gorenstein Projective Coresolutions and Co-Tate Homology Functors
Gorenstein Projective Coresolutions and Co-Tate Homology Functors
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For a local commutative Gorenstein ring R,Enochs et al.in[Gorenstein pro-jective resolvents,Comm.Algebra 44(2016)3989-4000]defined a functor(^)ExtRn(-,-)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(^)ExtRn(-,-)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 char-acterizations for the finiteness of RGpd(M).Then over a general ring R we define a co-Tate homology group(^)ExtRn(M,N)for R-modules M and N with RGpd(M)＜∞ and Gpd(N)＜∞,and prove that(^)ExtRn(M,N)can be computed by complete projective cores-olutions of the first variable or by complete projective resolutions of the second variable.
NETL
NSTL
万方数据
维普
