GI-模和余自反复形

doi:10.6040/j.issn.1671-9352.0.2019.458

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (4): 32-40.doi: 10.6040/j.issn.1671-9352.0.2019.458

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GI-模和余自反复形

刘妍平

西北师范大学经济学院, 甘肃兰州 730070

发布日期:2020-04-09
作者简介:刘妍平(1989— ),女,博士,副教授,研究方向为环的同调理论. E-mail:xbsdlyp@163.com
基金资助:
国家自然科学基金资助项目(11861055);西北师范大学青年教师科研能力提升计划资助项目(NWNU-LKQN-16-13)

GI-modules and coreflexive complexes

LIU Yan-ping

College of Economics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2020-04-09

摘要/Abstract

摘要： 研究GI-模和余自反复形及其性质,证明任意Artin模有有限的GI-维数当且仅当它作为复形是余自反的。同时研究复形的GI-维数,得到同调层次Artin的同调左有界复形的GI-维数有限当且仅当它是余自反的。

关键词: Gorenstein内射模, GI-类, 余自反复形, GI-维数

Abstract: A class of GI-modules, coreflexive complexes and their properties are investigated. It is proved that an artinian module has finite GI-dimension if and only if it is coreflexive as a complex. The GI-dimension of complexes is also studied and it is found that a complex homologically degreewise artinian and bounded to the left has finite GI-dimension if and only if it is coreflexive.

Key words: Gorenstein injective module, GI-class, coreflexive complex, GI-dimension

中图分类号:

O153.3

刘妍平. GI-模和余自反复形[J]. 《山东大学学报(理学版)》, 2020, 55(4): 32-40.

LIU Yan-ping. GI-modules and coreflexive complexes[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 32-40.

参考文献

[1] ENOCHS E E, JENDA O M G. On Gorenstein injective modules[J]. Communications in Algebra, 1993, 21(10):3489-3501.
[2] AUSLANDER M, BRIDGER M. Stable module theory[J]. Memoirs of the American Mathematical Society, 1969, 94(94):9-11.
[3] CHRISTENSEN L W. Gorenstein dimensions[M]. Berlin: Springer-Verlag, 2000.
[4] CHRISTENSEN L W, FRANKILD A, HOLM H. On Gorenstein projective, injective and flat dimensions: a functorial description with applications[J]. Journal of Algebra, 2006, 302(1):231-279.
[5] ENOCHS E E, JENDA O M G. Gorenstein injective and projective modules[J]. Mathematische Zeitschrift, 1995, 220(4):611-633.
[6] KHATAMI L, TOUSI M, YASSEMI S. Finiteness of Gorenstein injective dimension of modules[J]. Proceedings of the American Mathematical Society, 2009, 137(7):2201-2207.
[7] KHATAMI L, YASSEMI S. A Bass formula for Gorenstein injective dimension[J]. Communications in Algebra, 2007, 35(6):1882-1889.
[8] XU Jinzhong. Flat covers of modules[M]. Berlin: Springer-Verlag, 1996.
[9] HIREMATH V A. Coflat modules[J]. Indian Journal of Pure and Applied Mathematics, 1986, 17(2):223-230.
[10] ENOCHS EE, JENDA O M G. Relative homological algebra[M]. Berlin: Walter de Gruyter, 2000.
[11] SAZEEDEH R.Gorenstein injective modules and a generalization of Ischebeck formula[J]. Journal of Algebra and Its Applications, 2013, 12(4):1250197.
[12] CHRISTENSEN L W. Semi-dualizing complexes and their Auslander categories[J]. Transactions of the American Mathematical Society, 2001, 353(5):1839-1883.
[13] FRANKILD A, JORGENSEN P. Foxby equivalence, complete modules, and torsion modules[J]. Journal of Pure and Applied Algebra, 2002, 174(2):135-147.

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GI-模和余自反复形

GI-modules and coreflexive complexes

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