Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON WEAKLY S-PRIME SUBMODULES

  • Hani A., Khashan (Department of Mathematics Faculty of Science Al al-Bayt University) ;
  • Ece Yetkin, Celikel (Department of Basic Sciences Faculty of Engineering Hasan Kalyoncu University)
  • Received : 2021.10.27
  • Accepted : 2022.03.04
  • Published : 2022.11.30
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Abstract

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

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References

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