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F-本质子模与F-多余子模 被引量：2

F-ESSENTIAL SUBMODULES AND F-SUPERFLUOUS SUBMODULES
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摘要 本文研究了F-本质子模和F-多余子模.利用同调的方法,得到了F-本质与F-包络,F-多余与F-复盖之间的关系,另外还得到了F-本质子模,F-多余子模的相关性质,从而推广了文献[3,10]中的部分结果. This article study F-essential submodules and F-superfluous submodules.By homological methods,we obtain the relations between F-essential map and F-envelope（between F-superfluous map and F-cover）.Moreover,we show the relative properties of F-essential submodules and F-superfluous submodules,which generalize some results in [3,10].
作者 宋贤梅
机构地区 安徽师范大学数学系
出处 《数学杂志》 CSCD 北大核心 2012年第5期918-924,共7页 Journal of Mathematics
基金 国家自然科学基金资助(10571026) 安徽省教育厅重点研究项目资助(KJ2010A126)
关键词 F-本质子模 F-多余子模 F-包络 F-复盖 F-essential submodules F-superfluous submodules F-envelope F-cover
分类号 O153.3 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Bass H. Finitistic dimension and a homological generalization of semi-primary rings [J]. Trans. Amer. Math. Soc., 1960, 95: 466-488.
  • 2Enochs E E. Injective and flat covers, envelopes and resolvent [J]. Israel J. Math., 1981, 39:189-209.
  • 3Xu Jinzhong. Flat covers of modules [M]. Lecture Notes in Math. 1634, Berlin, Heideberg, New York: Springer-Verlag, 1996.
  • 4Trlifaj J. Covers, envelopes and cotorsion theories [M]. Lecture Notes for the Workshop "Homological Methods in Module Theory", Beijing, Nova Science Publishers, 2000.
  • 5Enochs E E, Jenda O M G. Relative homological algebra [M]. Berlin/New York: Walter de Gruyter, 2000.
  • 6Fay T, Jourbert S V. Relative injectiveity [J]. Chinese J. Math., 1994, 22(1): 65-94.
  • 7Anderson F W, Fuller K R. Rings and categories of modules [M]. Second Edition. Graduate Texts, Vol. 13, Berlin, Heidelberg, New York: Springer-Verlag~ 1992.
  • 8Bazzon S, Salce L. Strongly fiat covers [J]. J. London Math. Soc., 2002, 66(2): 276-294.
  • 9Ding Nanqing, Chen Jianlong. Relative covers and envelopes [J]. Acta. Math. Sinica, 1998, 41(3): 609-616.
  • 10Mao Lixin, Ding Nanqing. Notes on cotorsion modules [J]. Comm. Algrbra, 2005, 33(1): 349-360.

同被引文献9

  • 1佟文廷.同调代数引论[M]．北京：高等教育出版社，1996．
  • 2Bass H. Finitistic dimension and a homological of generalization of semi-primary rings[J]. Trans Am Math Soe, 1960,95:466.
  • 3Enochs E E. Injective and flat covers, envelopes and resolvent[J]. Israel J Math, 1981,39:189.
  • 4Xu Jinzhong. Flat covers of modules[M]. New York: Springer-Verlag, 1996.
  • 5Garcia Rozas J R. Covers and envelopes in the category of complexes of modules[M]. London: Chapman & Hall/CRC Press, 1999.
  • 6Bass H. Finitistic dimension and a homological of gen- eralization of semi-primary rings [ J ]. Trans. Amer. Math. Soc. , 1960,95:466-488.
  • 7Enochs E E. Injective and flat covers,envelopes and re- solvent[J]. Israel J. Math. ,1981,39:189-209.
  • 8Xu Jinzhong. Flat covers of modules [ M ]. Lecture Notes in Math. 1634, Berlin, Heideberg, New York: Springer- Verlag, 1996.
  • 9Garcta Rozas J R. Covers and envelopes in the category of complexes of modules [ M ]. Chapman & Hall/CRC Press,1999.

引证文献2

数学杂志
2012年 第5期

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