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Cm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(δCm)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.
Abstract
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 Cm 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 R-modules 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(δCm) is Gorenstein projective for all m∈Z. Similarly, Gorenstein injective and Gorenstein flat versions of all these results are given.
关键词
预包络 /
预覆盖 /
Gorenstein投射
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Key words
preenvelopes /
precovers /
Gorenstein projective
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参考文献
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