相对于半对偶模的Gorenstein平坦维数有限的模的Tate同调

doi:10.6040/j.issn.1671-9352.0.2018.719

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 102-105.doi: 10.6040/j.issn.1671-9352.0.2018.719

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相对于半对偶模的Gorenstein平坦维数有限的模的Tate同调

潘晓玲,梁力^*

兰州交通大学数理学院, 甘肃兰州 730070

发布日期:2019-12-11
作者简介:潘晓玲(1993— ),女,硕士研究生,研究方向为同调代数. E-mail:945558362@qq.com*通信作者简介: 梁力(1980— ), 男, 博士, 教授, 研究方向为同调代数. E-mail:lliang@mail.lzjtu.cn
基金资助:
国家自然科学基金资助项目(11761045,11561039);兰州交通大学“百名青年优秀人才培养计划"基金资助项目;甘肃省自然科学基金资助项目(18JR3RA113,17JR5RA091)

Tate homology of modules of finite Gorenstein flat dimension with respect to a semidualizing module

PAN Xiao-ling, LIANG Li^*

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Published:2019-12-11

摘要/Abstract

摘要： 对于半对偶模C, 研究了具有Tate F_C-分解的模的Tate同调Tor^F_C。特别地, 建立了一个连接 Tor^F_C, Tor^F_C 和 Tor^GF_C 的长正合列。作为应用, 证明了该Tate同调 Tor^F_C的vanishing性和平衡性。

关键词: 半对偶模, Tate F_C-分解, Tate F_C-同调

Abstract: For a semidualing module C, Tate homology Tor^F_C of modules admitting Tate F_C-resolutions is investigated. In particular, a long exact sequence connecting Tor^F_C, Tor^F_C and Tor^GF_C is built. As applications, the vanishing and the balance of this Tate homology theory are proved.

Key words: semidualizing module, Tate F_C-resolution, Tate F_C-homology

中图分类号:

O154.2

潘晓玲,梁力. 相对于半对偶模的Gorenstein平坦维数有限的模的Tate同调[J]. 《山东大学学报(理学版)》, 2019, 54(12): 102-105.

PAN Xiao-ling, LIANG Li. Tate homology of modules of finite Gorenstein flat dimension with respect to a semidualizing module[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 102-105.

参考文献

[1] SATHER-WAGSTAFF S, SHARIF T, WHITE D. Tate cohomology with respect to semidulizing modules[J]. J Algebra, 2010, 324:2336-2368.
[2] HU Jiangsheng, GENG Yuxian, DING Nanqing. Tate cohomology of Gorenstein flat modules with respect to semidulizing modules[J]. Rocky Mountain J Math, 2017, 47:205-238.
[3] LIANG Li. Tate homology of modules of finite Gorenstein flat dimension[J]. Algebra Represent Theor, 2013, 16:1541-1560.
[4] SALIMI M, SATHER-WAGSTAFF S, TAVASOLI E, et al. Relative Tor functors with respect to a semidualizing module[J]. Algebra Represent Theor, 2014, 17:103-120.

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相对于半对偶模的Gorenstein平坦维数有限的模的Tate同调

Tate homology of modules of finite Gorenstein flat dimension with respect to a semidualizing module

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