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BALANCE FOR TATE COHOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES
Published online by Cambridge University Press: 18 July 2013
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.
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- Copyright ©2013 Australian Mathematical Publishing Association Inc.
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