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山东大学学报(理学版) ›› 2015, Vol. 50 ›› Issue (10): 68-75.doi: 10.6040/j.issn.1671-9352.0.2014.449

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Gorenstein弱平坦模

饶炎平, 杨刚   

  1. 兰州交通大学数理学院, 甘肃 兰州 730070
  • 收稿日期:2014-10-13 修回日期:2015-03-27 出版日期:2015-10-20 发布日期:2015-10-21
  • 作者简介:饶炎平(1988-),男,硕士研究生,研究方向为同调代数.E-mail:yprao0213@gmail.com
  • 基金资助:
    国家自然科学基金资助项目(11101197);甘肃省自然科学基金资助项目(145RJZA079)

Gorenstein weak flat modules

RAO Yan-ping, YANG Gang   

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2014-10-13 Revised:2015-03-27 Online:2015-10-20 Published:2015-10-21

摘要: 引入了Gorenstein弱平坦模,给出了Gorenstein弱平坦模的一些性质。证明了Gorenstein弱平坦模类关于直积封闭,Gorenstein弱平坦模类是投射可解类当且仅当它关于扩张封闭,并且证明了每一个模都具有Gorenstein弱平坦预覆盖。

关键词: 弱平坦模, Gorenstein弱平坦预覆盖, IF环, Gorenstein弱平坦模

Abstract: Gorenstein weak flat modules are introduced and some properties of such modules are given. It is proved that the class of Gorenstein weak flat modules is closed under direct products, and that the class of Gorenstein weak flat modules is projectively resolving if and only if it is closed under extensions. Moreover, it is proved that every module has a Gorenstein weak flat precover.

Key words: weak flat module, Gorenstein weak flat precover, IF ring, Gorenstein weak flat module

中图分类号: 

  • O153.3
[1] ROTMAN J J. An introduction to Homological algebra[M]. New York: Academic Press, 1979.
[2] ENOCHS E E, JENDA O M G, TORRECILLAS B. Gorenstein flat modules[J]. Journal of Nanjing University: Natural Science, 1993, 10(1):1-9.
[3] ENOCHS E E, JENDA O M G. Gorenstein injective and projective modules[J]. Math Z, 1995, 220(1):611-633.
[4] HOLM H. Gorenstein homological dimensions[J]. J Pure Appl Algebra, 2004, 189(1):167-193.
[5] BENNIS D. Rings over which the class of Gorenstein flat modules is closed under extensions[J]. Comm Algebra, 2009, 37:855-868.
[6] BENNIS D. Weak Gorenstein global dimension[J]. Int Electron J Algebra, 2010, 8:140-152.
[7] GAO Zenghui. Weak Gorenstein projective, injective and flat modules[J]. J Algebra Appl, 2013, 12(2):1250165.1-1250165.15.
[8] GAO Zenghui, WANG Fanggui. All Gorenstein hereditary rings are coherent[J]. J Algebra Appl, 2014, 13(4):1350140.1-1350140.5.
[9] GAO Zenghui, WANG Fanggui. Weak injective and weak flat modules[J]. Comm Algebra, 2015, 43(9):3857-3868.
[10] ENOCHS E E, JENDA O M G. Relative homological algebra[M].Berlin:Walter de Gruyer, 2000.
[11] GARCÍA ROZAS J R. Covers and envelope in the category of complexes of modules[M]. New York: CRC Press, 1999.
[12] COLBY R R. Rings which have flat injective modules[J]. J Algebra, 1975, 35:239-252.
[13] ENOCHS E E, LÓPEZ-RAMOS J A. Kaplansky classes[J]. Rend Sem Mat Univ Padova, 2002, 107:67-79.
[14] GILLESPIE J. The flat model structure on Ch(R)[J]. Trans Amer Math Soc, 2004, 356:3369-3390.
[15] WANG Z P, LIU Z K. Complete cotorsion pairs in the category of complexes[J]. Turk J Math, 2013, 37:852-862.
[16] ALDRICH S T, ENOCHS E E, GARCA ROZAS J R, et al. Covers and envelopes in Grothendieck categories: flat covers of complexes with applications[J]. J Algebra, 2001, 243:615-630.
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