模的Gorenstein cotorsion包络

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英文篇名：Gorenstein cotorsion envelope of modules 作者：张豫冈 英文作者：Zhang Yugang;Department of Basic Sciences Lanzhou Institute Technology; 关键词：Gorenstein ; cotorsion模 ; (预)包络 ; 基本扩张 英文关键词：Gorenstein cotorsion modules,(pre)envelope,essential extension 中文刊名：CCSX 英文刊名：Pure and Applied Mathematics 机构：兰州工业学院基础学科部; 出版日期：2014-04-25 出版单位：纯粹数学与应用数学 年：2014 期：v.30 基金：国家自然科学基金(11101197) 语种：中文; 页：CCSX201402008 页数：5 CN：02 ISSN：61-1240/O1 分类号：67-71

摘要

通过与模的内射包络相比较,讨论了模的基本扩张与Gorenstein cotorsion包络及单模的Gorenstein cotorsion包络,给出了模的Gorenstein cotorsion包络具有类似性质的一些充分条件.
        Comparing with injective envelope of modules, we discuss the essential extension of modules and Gorenstein cotorsion envelope as well as Gorenstein cotorsion envelope of simple modules. Some sufficient conditions under which the properties of Gorenstein cotorsion envelope analogous to those of injective envelope are given.

引文

[1]Enochs E E,Jenda O M G.Relative Homological Algebra[M].Berlin:Springer-Verlag,2000.
    [2]Holm H.Gorenstein homological dimensions[J].J.Pure Appl.Algebra,2004,189:167-193.
    [3]Mao L X,Ding N Q.Gorenstein FP-injective and Gorenstein flat modules[J].Journal of Algebra and Its Applications,2008,7(4):491-506.
    [4]Enochs E E,Jenda O M G,Torrecillas B.Gorenstein flat modules[J].南京大学学报:数学半年刊,1993,10:1-9.
    [5]Bennis D.Rings over which the class of Gorenstein flat modules is closed under extensions[J].Comm.Algebra,2009,37(3):181-190.
    [6]Yang G,Liu Z K.Gorenstein flat cover over GF-closed rings[J].Comm.Algebra,2012,40(5):1632-1640.
    [7]Rotman J.An introduction to Homological Algebra[M].New york:Academic Press,1979.
    [8]Anderson F W,Fuller K R.Rings and Categories of Modules[M].2nd ed.New York:Springer,1992.