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BALANCE FOR TATE COHOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES

Part of: Homological algebra Commutative algebra: Homological methods

Published online by Cambridge University Press:  18 July 2013

LI LIANG  and
GANG YANG
LI LIANG*
Affiliation:
School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, PR China email yanggang@mail.lzjtu.cn
GANG YANG
Affiliation:
School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, PR China email yanggang@mail.lzjtu.cn
*
✉lliangnju@gmail.com
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Abstract

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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.

Keywords

Tate cohomologyrelative cohomologybalancesemidualizing modules

MSC classification

Secondary: 13D07: Homological functors on modules (Tor, Ext, etc.) 18G15: Ext and Tor, generalizations, Künneth formula 18G25: Relative homological algebra, projective classes 13D02: Syzygies, resolutions, complexes 13D05: Homological dimension 18G10: Resolutions; derived functors 18G20: Homological dimension
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 2 , October 2013 , pp. 223 - 240
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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