ISSN 0253-2778

CN 34-1054/N

open
Free to Publish. Free to Read.
Open AccessOpen Access JUSTC Original Paper

On GI-flat and GF-torsion modules

  • 1.

    School of Finance and Mathematics, West Anhui University, Luan 237012, China

  • 2.

    College of Mathematics, Qingdao University, Qingdao 266071, China

  • 3.

    School of Mathematical Sciences, Anhui University, Hefei 230039, China

Cite this: JUSTC, 2015, 45(3): 193-198
https://doi.org/10.3969/j.issn.0253-2778.2015.03.003
Funds: Supported by the Key Program of Excellent Youth Foundation of Higher Education in Anhui Province (2013SQRL071ZD), the National Natural Science Foundation of China (11126173).
More Information
  • Author Bio:

    WANG Xiujian, male, born in 1982, PhD/lecturer. Research field: ring and algebra representation. E-mail:xjwang@wxc.edu.cn

  • Corresponding author:

    DU Xianneng

  • Received Date: February 04, 2013
  • Revised Date: March 02, 2014
  • Accepted Date: March 02, 2014
  • Published Date: March 29, 2015
    Abstract
  • Two classes of modules were studied: GI-flat and GF-torsion modules, where GI stands for Gorenstein injective modules and GF for Gorenstein flat modules. Two homological dimensions for a ring were investigated, the supremum of the flat dimension of Gorenstein injective modules and the supremum of the GF-torsion dimension of all modules. The relation between these classes of modules and the homological dimensions was also studied.
    • FullText(HTML)
    References (17)
    Related Articles
    Track Citations

Catalog

    Get Citation
    {{if article.pdfAccess}}
    {{if article.articleBusiness.pdfLink && article.articleBusiness.pdfLink != ''}} {{else}} {{/if}}PDF
    {{/if}}
    XML
    [1]
    Enochs E, Jenda O. On Gorenstein injective modules and projective modules[J]. Math Z, 1995, 220: 611-633.
    [2]
    Bennis D, Mahdou N. Strongly Gorenstein projective, injective and at modules[J]. J Pure Appl Algebra, 2007, 210: 437-445.
    [3]
    Gao Z H. Universal Gorenstein homological methods and its applications[D]. Chengdu: Sichuan Normal University, 2011.
    [4]
    Enochs E E, Jenda O M G. Copure injective resolutions, flat resolvents and dimensions[J]. Comment Math Univ Carolin, 1993, 34:203-211.
    [5]
    Gao Z H. On GI-flat modules and dimensions[J]. J Korean Math Soc, 2013, 50: 203-218.
    [6]
    Song W L, Huang Z Y. Gorenstein atness and injectivity over Gorenstein rings[J]. Science in China Series A: Mathematics, 2008, 51:215-218.
    [7]
    Chen J, Ding N. The flat dimensions of injective modules[J]. Manuscripta Math, 1993, 78:165-177.
    [8]
    Holm H. Gorenstein homological dimension[J]. J Pure Appl Algebra, 2004, 189: 167-193.
    [9]
    Tong W T. An Introduction to Homological Algebra[M]. Beijing: Higher Education Press, 1998.
    [10]
    Mahdou N, Tamekkante M, Yassemi S. On (strongly) Gorenstein Von Neumann regular rings[J]. Comm in Algebra, 2011, 39: 3 242-3 252.
    [11]
    Holm H. Rings with finite Gorenstein injective dimension[J]. Proc Amer Marh Soc, 2003, 132: 1 279-1 283.
    [12]
    Mahdou N, Tamekkante M. The orthogonal complement relative to the functor extension of the class of all Gorenstein at modules[J]. Adv Pure Appl Math, 2011, 2: 133-145.
    [13]
    Bennis D. Rings over which the class of Gorenstein at modules is closed under extensions[J]. Comm in Algebra, 2009, 37: 855-868.
    [14]
    Mahdou N, Tamekkante M. On (strongly) Gorenstein (semi)hereditary rings[J]. Arab J Sci Eng, 2011, 36: 431-440.
    [15]
    Bennis D, Mahdou N. Global Gorenstein dimensions[J] Proc Amer Math Soc, 2010, 138: 461-465.
    [16]
    Pan Q X, Zhu X L. GP-projective and GI-injective modules[J]. Math Notes, 2012, 91: 824-832.
    [17]
    Bennis D, Mahdou N. A generalization of strongly Gorenstein projective module[J]. J Algebra and Its Appl, 2009, 8: 219-227.

    Related Articles

    [1]Haonan He, Jiaxin Sun, Chaojia Zhang, Jie Zhao, Shanyong Wang. Optimizing convergence for dual-credit policy and carbon trading in the automobile sector: A bi-layer planning model[J]. JUSTC, 2023, 53(8): 0805. DOI: 10.52396/JUSTC-2023-0038
    [2]Ma Yulian, Cui Wenquan. An end-to-end multitask method with two targets for high-frequency price movement prediction[J]. JUSTC, 2021, 51(3): 246-258. DOI: 10.52396/JUST-2021-0052
    [3]He Haonan, Ren Wei, Wang Zuohang, Zhao Chenyong, Wang Shanyong, Ma Fei. Effect of personal carbon trading on EV adoption behavior based on a stochastic Petri net[J]. JUSTC, 2021, 51(1): 53-64. DOI: 10.52396/JUST-2020-0024
    [4]MENG Xuran, BI Xiuchun, ZHANG Shuguang. High frequency algorithm and its back-testing results based on GAN[J]. JUSTC, 2020, 50(6): 801-810. DOI: 10.3969/j.issn.0253-2778.2020.06.012
    [5]YU Xiaoyu, BI Xiuchun, ZHANG Shuguang. Optimal threshold of pairs trading[J]. JUSTC, 2020, 50(6): 784-792. DOI: 10.3969/j.issn.0253-2778.2020.06.010
    [6]ZENG Weihui, LI Miao, ZHANG Jian, HUANG Xiaoping, WANG Jingxian, YUAN Yuan. Research on high-order residual convolution neural network for crop disease recognition application[J]. JUSTC, 2019, 49(10): 781-790. DOI: 10.3969/j.issn.0253-2778.2019.10.002
    [7]DENG Xinning, BI Xiuchun, ZHANG Shuguang. Optimal dynamic cointegrated pairs trading strategies with state-dependent risk aversion[J]. JUSTC, 2019, 49(8): 655-667. DOI: 10.3969/j.issn.0253-2778.2019.08.009
    [8]LONG Aoming, BI Xiuchun, ZHANG Shuguang. An arbitrage strategy model for ferrous metal futures based on LSTM neural network[J]. JUSTC, 2018, 48(2): 125-132. DOI: 10.3969/j.issn.0253-2778.2018.02.006
    [9]LUO Kebing, YE Wuyi, DONG Xiaowen. Granger causality test in quantiles and conditional VaR estimation of continuously rising and falling returns[J]. JUSTC, 2016, 46(11): 919-927. DOI: 10.3969/j.issn.0253-2778.2016.11.007
    [10]WANG Libin, FANG Zhaoben. Empirical research on persistence of Chinas stock market price using ultra-high frequency data[J]. JUSTC, 2015, 45(5): 422-428. DOI: 10.3969/j.issn.0253-2778.2015.05.012
    TrendMD
    Volume 45 Issue 3 PP. 193-198
    Cover

    Article Metrics

    Article views (132) PDF downloads (161)

    Copyright © Editorial Office of JUSTC, All Rights Reserved. 皖ICP备05002528号

    Supported by: Beijing Renhe Information Technology Co., Ltd.  Baidu Analytics

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return