JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (10): 22-26.doi: 10.6040/j.issn.1671-9352.0.2018.147

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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

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

CLC Number: 

  • O153.3
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