Complete cohomology for complexes with finite Gorenstein AC-projective dimension |
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| Authors: | Jiangsheng Hu Yuxian Geng Qinghua Jiang |
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| Affiliation: | 1. School of Mathematics Sciences, Nanjing Normal University, Nanjing 210046, China2. School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China3. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China |
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| Abstract: | We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite Gorenstein AC-projective dimension. This lets us give some general techniques for computing complete cohomology of complexes with finite Gorenstein AC-projective dimension. As a consequence, the classical relative cohomology for modules of finite Gorenstein AC-projective dimension is extended. Finally, the relationships between projective dimension and Gorenstein AC-projective dimension for complexes are given. |
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| Keywords: | Gorenstein AC-projective complete level resolution complete cohomology |
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