## Rocky Mountain Journal of Mathematics

### Tate cohomology of Gorenstein flat modules with respect to semidualizing modules

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 3 March 2017

https://projecteuclid.org/euclid.rmjm/1488531897

Digital Object Identifier
doi:10.1216/RMJ-2017-47-1-205

Mathematical Reviews number (MathSciNet)
MR3619761

Zentralblatt MATH identifier
1371.13029

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1488531897

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