| Vanishing of Tate Homology — An Application of Stable Homology for Complexes |
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| 基金项目： | Supported by National Natural Science Foundation of China (Grant Nos. 11261050, 11361051 and 11501451) and Program for New Century Excellent Talents in University (Grant No. NCET-13-0957) |
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| 摘 要： | It has been proved that the vanishing of Tate homology is a sufficient condition for the derived depth formula to hold in J. Pure Appl. Algebra, 219, 464–481(2015)]. In this paper, we investigate when Tate homology vanishes by studying the stable homology theory for complexes. Properties such as the balancedness and vanishing of stable homology for complexes are studied. Our results show that the vanishing of this homology can detect finiteness of homological dimensions of complexes and regularness of rings.
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