BALANCE FOR TATE COHOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES
BALANCE FOR TATE COHOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES
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DOI：
10.1017/s1446788713000232
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发表时间：
2013-07
影响因子：
0.7
通讯作者：
L. Liang;Gang Yang
中科院分区：
文献类型：
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作者：
L. Liang;Gang Yang
本文利用Sather-WagStaff等人的理想，进一步研究了交换环上模关于半对偶模的Tate上同调。[‘关于半对偶化模的Tate上同调’，J.Algebra 324(2010)，2336-2368]。特别地，我们证明了对任意$n\in\mathbb{Z}$，Tate上同调${\widehat{\mathm{Ext}}^{n}$有一个平衡结果。这一结果补充了Sather-WagStaff等人的工作，他们证明了这一结果对任何$n\geq 1$都成立。我们还讨论了Tate上同调的一些消失性。
Abstract In this paper, we further study Tate cohomology of modules over a commutative ring with respect to semidualizing modules using the ideals of Sather-Wagstaff et al. [‘Tate cohomology with respect to semidualizing modules’, J. Algebra 324 (2010), 2336–2368]. In particular, we prove a balance result for the Tate cohomology ${\widehat{\mathrm{Ext} }}^{n} $ for any $n\in \mathbb{Z} $. This result complements the work of Sather-Wagstaff et al., who proved that the result holds for any $n\geq 1$. We also discuss some vanishing properties of Tate cohomology.