Vanishing of stable homology with respect to a semidualizing module

We investigate stable homology of modules over a commutative noetherian ring R with respect to a semidualzing module C, and give some vanishing results that improve/extend the known results. As a consequence, we show that the balance of the theory forces C to be trivial and R to be Gorenstein.

相对于半对偶模的Gorenstein平坦维数有限的模的Tate同调

对于半对偶模C,研究了具有Tate FC-分解的模的Tate同调■。特别地,建立了一个连接■和TorGFC的长正合列。作为应用,证明了该Tate同调■的vanishing性和平衡性。