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BALANCE FOR TATE COHOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 95 / Issue 2 / October 2013
- Published online by Cambridge University Press:
- 18 July 2013, pp. 223-240
- Print publication:
- October 2013
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- Article
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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.
