Rocky Mountain Journal of Mathematics

Tate cohomology of Gorenstein flat modules with respect to semidualizing modules

Jiangsheng Hu, Yuxian Geng, and Nanqing Ding

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We study Tate cohomology of modules over a commutative Noetherian ring with respect to semidualizing modules. First, we show that the class of modules admitting a Tate $\mathcal{F}_C $-resolution is exactly the class of modules in $\mathcal{B}_{C} $ with finite $\mathcal{GF}_{C} $-projective dimension. Then, the interaction between the corresponding relative and Tate cohomologies of modules is given. Finally, we give some new characterizations of modules with finite $\mathcal{F}_C $-projective dimension.

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Rocky Mountain J. Math., Volume 47, Number 1 (2017), 205-238.

First available in Project Euclid: 3 March 2017

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Zentralblatt MATH identifier

Primary: 16E05: Syzygies, resolutions, complexes 18G20: Homological dimension [See also 13D05, 16E10] 18G35: Chain complexes [See also 18E30, 55U15]

$C$-Gorenstein flat module semidualizing module Tate cohomology


Hu, Jiangsheng; Geng, Yuxian; Ding, Nanqing. Tate cohomology of Gorenstein flat modules with respect to semidualizing modules. Rocky Mountain J. Math. 47 (2017), no. 1, 205--238. doi:10.1216/RMJ-2017-47-1-205.

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