Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON WEAKLY QUASI n-ABSORBING SUBMODULES

  • Issoual, Mohammed (Laboratory of Modeling and Mathematical Structures Department of Mathematics Faculty of Science and Technology of Fez University S.M. Ben Abdellah Fez) ;
  • Mahdou, Najib (Laboratory of Modeling and Mathematical Structures Department of Mathematics Faculty of Science and Technology of Fez University S.M. Ben Abdellah Fez) ;
  • Moutui, Moutu Abdou Salam (Division of Science, Technology, and Mathematics American University of Afghanistan)
  • Received : 2021.01.03
  • Accepted : 2021.03.08
  • Published : 2021.11.30
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Abstract

Let R be a commutative ring with 1 ≠ 0, n be a positive integer and M be an R-module. In this paper, we introduce the concept of weakly quasi n-absorbing submodule which is a proper generalization of quasi n-absorbing submodule. We define a proper submodule N of M to be a weakly quasi n-absorbing submodule if whenever a ∈ R and x ∈ M with 0 ≠ an x ∈ N, then an ∈ (N :R M) or an-1 x ∈ N. We study the basic properties of this notion and establish several characterizations.

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References

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