JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (10): 68-75.doi: 10.6040/j.issn.1671-9352.0.2014.449

Previous Articles     Next Articles

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

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

CLC Number: 

  • 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.
[1] CHEN Wen-jing, LIU Zhong-kui. Remarks on n-strongly Gorenstein FP-injective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 50-54.
Full text



No Suggested Reading articles found!