JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 38-42.doi: 10.6040/j.issn.1671-9352.0.2022.630

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Gorenstein cotorsion modules of Noetherian rings

Yadong LUO(),Gang YANG*()   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2022-11-28 Online:2023-08-20 Published:2023-07-28
  • Contact: Gang YANG E-mail:1264054907@qq.com;yanggang@mail.lzjtu.cn

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Abstract:

Let R be a left Noetherian ring. It is proved that if the Gorenstein flat cover of any injective precover of a left R-module M is injective, then the Gorenstein flat cover of M is injective if and only if every injective f : E→M of M is surjective and Ker f is Gorenstein cotorsion.

Key words: injective modules, Gorenstein flat modules, Gorenstein cotorsion modules, strongly Gorenstein cotorsion modules

CLC Number: 

  • O154.2
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