Complete cohomology for complexes with finite Gorenstein AC-projective dimension

作     者：Jiangsheng HU Yuxian GENG Qinghua JIANG 无

作者机构：School of Mathematics Sciences Nanjing Normal University Nanjing 210046 China School of Mathematics and Physics Jiangsu University of Technology Changzhou 213001China School of Mathematics and Quantitative Economics Shandong University ofFinance and Economics Jinan 250014 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2016年第11卷第4期

页      面：901-920页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 080502[工学-材料学] 0701[理学-数学] 

基　　金：This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11371187  11501257) and Jiangsu University of Technology of China (KYY14015  KYY14016) 

主　　题：Gorenstein AC-projective complete level resolution complete cohomology 

摘      要：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.