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山东大学学报(理学版) ›› 2018, Vol. 53 ›› Issue (10): 22-26.doi: 10.6040/j.issn.1671-9352.0.2018.147

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分次版本的Enochs定理

吴小英,王芳贵*   

  1. 四川师范大学数学学院, 四川 成都 610068
  • 收稿日期:2018-03-22 出版日期:2018-10-20 发布日期:2018-10-09
  • 作者简介:吴小英(1992— ), 女, 硕士研究生, 研究方向为分次环与分次模的研究. E-mail: mengwxy2017@163.com*通信作者简介:王芳贵(1955— ), 男, 教授, 研究方向为交换代数与同调代数理论的研究. E-mail:wangfg2004@163.com
  • 基金资助:
    国家自然科学基金资助项目(11671283)

Graded version of Enochs theorem

WU Xiao-ying, WANG Fang-gui*   

  1. College of Mathematics, Sichuan Normal University, Chengdu 610068, Sichuan, China
  • Received:2018-03-22 Online:2018-10-20 Published:2018-10-09

摘要: 证明了分次版本的Enochs定理: 设A是有限生成分次R-B的分次子模, 若对任何FP-gr-内射 R-E, 分次同态f:A→E恒能扩张到B, A是有限生成的由此得到有限生成分次R-M是有限表现的当且仅当对任何FP-gr-内射模E, 都有EXT1R(M,E)=0

关键词: 有限表现模, FP-内射模, FP-gr-内射模, 分次超有限表现模

Abstract: It is shown that graded version of Enochs theorem is proved. Let B be a finitely generated graded R-module and let A be a graded submodule of B. If every graded homomorphsim f: A→E can be extended to B for any FP-gr-injective R-module E, then A is finitely generated. It follows that a finitely generated graded R-module M is finitely presented if and only if EXT1R(M,E)=0 for any FP-gr-injective module E.

Key words: FP-injective module, graded super finitely presented module, FP-gr-injective module, finitely presented module

中图分类号: 

  • O153.3
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