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山东大学学报(理学版) ›› 2018, Vol. 53 ›› Issue (6): 1-6.doi: 10.6040/j.issn.1671-9352.0.2017.524

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复形的 FR-内射维数与 FR-平坦维数

卢博, 禄鹏   

  1. 西北民族大学数学与计算机科学学院, 甘肃 兰州 730030
  • 收稿日期:2017-07-15 出版日期:2018-06-20 发布日期:2018-06-13
  • 作者简介:卢博(1985— ), 男, 副教授, 博士研究生, 研究方向为同调代数. E-mail: lubo55@126.com
  • 基金资助:
    国家自然科学基金资助项目(11501451);西北民族大学引进人才项目(XBMUYJRC201406)

FR-injective and FR-flat dimensions of complexes

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Received:2017-07-15 Online:2018-06-20 Published:2018-06-13

摘要: 引入并研究了复形的 FR-内射维数与 FR-平坦维数, 借助相应的余挠对得到了两个新的 Quillen 模型结构。

关键词: 模型结构, FR-内射(投射)维数, FR-平坦(余挠)维数

Abstract: The notion of FR-injective and FR-flat dimensions of complexes is introduced and investigated. Two new Quillen model structures are also obtained by means of corresponding cotorsion pairs.

Key words: FR-injective(projective)dimension, FR-flat(cotorsion)dimension, model structure

中图分类号: 

  • O154.2
[1] AVRAMOV L L, FOXBY H B. Homological dimensions of unbounded complexes[J]. Journal of Pure & Applied Algebra, 1991, 71(2/3):129-155.
[2] CHRISTENSEN L W. Gorenstein dimensions[M]. Berlin: Springer-Verlag, 2000.
[3] VELICHE O. Gorenstein projective dimension for complexes[J]. Transactions of the American Mathematical Society, 2006, 358(3):1257-1283.
[4] ASADOLLAHI J, SALARIAN Sh. Cohomology theories based on Gorenstein injective modules[J]. Trans Amer Math Soc, 2006, 358(5): 2183-2203.
[5] LIU Zhongkui, REN Wei. Transfer of Gorenstein dimensions of unbounded complexes along ring homomorphisms[J]. Comm. Algebra, 2014, 42(8): 3325-3338.
[6] LU Bo, LIU Zhongkui. Relative injectivity and flatness of complexes[J]. Kodai Math J, 2013, 36(2): 343-362.
[7] GARCÍA R J R. Covers and envelopes in the category of complexes of modules[M]. Chapman & Hall/CRC Press, 1999.
[8] ENOCHS E E, OYONARTE L. Covers, envelopes and cotorsion theories[M]. New York: Nova Science Publishere, 2002.
[9] COSTA D L. Parameterizing families of non-noetherian rings[J]. Comm Algebra, 1994, 22(10): 3997-4011.
[10] MAO Lixin, DING Nanqing. Relative projective modules and relative injective modules[J]. Comm Algebra, 2006, 34(7): 2403-2418.
[11] ZHOU Dexu. On n-coherent rings and(n, d)-rings[J]. Comm Algebra, 2004, 32(6): 2425-2441.
[12] GILLESPIE J. The flat model structure on Ch(R)[J]. Trans Amer Math Soc, 2004, 356(8): 3369-3390.
[13] VERDIER J L. Cat'egories D'eriv'ees[M]. Lecture Notes in Math, 569, Berlin: Springer-Verlag, 1977: 262-311.
[14] 章璞. 三角范畴与导出范畴[M].北京:科学出版社, 2015:110-135. ZHANG Pu. Triangulated categories and derived categories[M]. Beijing: Science Press, 2015:110-135.
[15] HOVEY M. Model categories[M]. Mathematical Surveys and Monographs, 63, Providence, RI: American Mathematical Society, 1999.
[16] HOVEY M. Cotorsion pairs, model category structures, and representation theory[J]. Math Z, 2002, 241(3): 553-592.
[17] YANG Gang, LIU Zhongkui. Cotorsion pairs and model structure on Ch(R)[J]. Proc Edinb Math Soc, 2011, 54(3): 783-797.
[18] 任伟. 复形范畴与三角范畴中的相对同调维数[D].兰州:西北师范大学, 2013. REN Wei. Relative homological dimensions in the category of complexes and triangulated categories[D]. Lanzhou: Northwest Normal University, 2013.
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