Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE CLASS OF WEAK w-PROJECTIVE MODULES IS A PRECOVER

  • Kim, Hwankoo (Division of Computer Engineering Hoseo University) ;
  • Qiao, Lei (College of Mathematics and Software Science Sichuan Normal University) ;
  • Wang, Fanggui (College of Mathematics and Software Science Sichuan Normal University)
  • Received : 2021.02.21
  • Accepted : 2021.10.14
  • Published : 2022.01.31
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Abstract

Let R be a commutative ring with identity. Denote by w𝒫w the class of weak w-projective R-modules and by w𝒫w⊥ the right orthogonal complement of w𝒫w. It is shown that (w𝒫w, w𝒫w⊥) is a hereditary and complete cotorsion theory, and so every R-module has a special weak w-projective precover. We also give some necessary and sufficient conditions for weak w-projective modules to be w-projective. Finally it is shown that when we discuss the existence of a weak w-projective cover of a module, it is enough to consider the w-envelope of the module.

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Acknowledgement

The authors would like to express their sincere thanks for the referee for his/her careful reading and helpful comments. This research was supported by the Academic Research Fund of Hoseo University in 2019 (20190817).

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