Gorenstein投射、内射和平坦复形

证明了在任意结合环R上,复形C是Gorenstein投射复形当且仅当每个层次的模C~m是Gorenstein投射模,由此给出了复形Gorenstein投射维数的性质刻画.并证明了对于正合复形C,若对于任意投射模Q,函子Hom(-,Q)作用复形C后仍然得到正合复形,则C是Gorenstein投射复形当且仅当对于所有的m∈Z,有Ker(δ_C~m)是Gorenstein投射模.类似地,本文也讨论了关于Gorenstein内射和Gorenstein平坦复形的相应结果.

Gorenstein Projective,Injective and Flat Complexes

It is shown in the paper that for a general associative ring R,any complex C of R-modules is Gorenstein projective if and only if each R-module C~m is Gorenstein projective for all m∈Z,as immediate consequences of the result,Gorenstein projective dimensions of complexes are characterized.Furthermore,if C is an exact complex of Rmodules such that this sequence remains exact when the functor Hom(—,Q)is applied to it for any projective R-module Q,then C is Gorenstein projective if and only if each Ker(δ_C~m)is Gorenstein projective for all m∈Z.Similarly,Gorenstein injective and Gorenstein flat versions of all these results are given.