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- 2018
复形的 FR-内射维数与 FR-平坦维数
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Abstract:
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。
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
| [1] | ASADOLLAHI J, SALARIAN Sh. Cohomology theories based on Gorenstein injective modules[J]. Trans Amer Math Soc, 2006, 358(5): 2183-2203. |
| [2] | LIU Zhongkui, REN Wei. Transfer of Gorenstein dimensions of unbounded complexes along ring homomorphisms[J]. Comm. Algebra, 2014, 42(8): 3325-3338. |
| [3] | GARCíA R J R. Covers and envelopes in the category of complexes of modules[M]. Chapman & Hall/CRC Press, 1999. |
| [4] | YANG Gang, LIU Zhongkui. Cotorsion pairs and model structure on Ch(R)[J]. Proc Edinb Math Soc, 2011, 54(3): 783-797. |
| [5] | AVRAMOV L L, FOXBY H B. Homological dimensions of unbounded complexes[J]. Journal of Pure & Applied Algebra, 1991, 71(2/3):129-155. |
| [6] | LU Bo, LIU Zhongkui. Relative injectivity and flatness of complexes[J]. Kodai Math J, 2013, 36(2): 343-362. |
| [7] | ENOCHS E E, OYONARTE L. Covers, envelopes and cotorsion theories[M]. New York: Nova Science Publishere, 2002. |
| [8] | COSTA D L. Parameterizing families of non-noetherian rings[J]. Comm Algebra, 1994, 22(10): 3997-4011. |
| [9] | MAO Lixin, DING Nanqing. Relative projective modules and relative injective modules[J]. Comm Algebra, 2006, 34(7): 2403-2418. |
| [10] | VERDIER J L. Cat'egories D'eriv'ees[M]. Lecture Notes in Math, 569, Berlin: Springer-Verlag, 1977: 262-311. |
| [11] | 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. |
| [12] | GILLESPIE J. The flat model structure on Ch(R)[J]. Trans Amer Math Soc, 2004, 356(8): 3369-3390. |
| [13] | CHRISTENSEN L W. Gorenstein dimensions[M]. Berlin: Springer-Verlag, 2000. |
| [14] | VELICHE O. Gorenstein projective dimension for complexes[J]. Transactions of the American Mathematical Society, 2006, 358(3):1257-1283. |
| [15] | ZHOU Dexu. On <i>n</i>-coherent rings and(<i>n, d</i>)-rings[J]. Comm Algebra, 2004, 32(6): 2425-2441. |
| [16] | HOVEY M. Model categories[M]. Mathematical Surveys and Monographs, 63, Providence, RI: American Mathematical Society, 1999. |
| [17] | HOVEY M. Cotorsion pairs, model category structures, and representation theory[J]. Math Z, 2002, 241(3): 553-592. |
| [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. |
