Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE STRUCTURE OF A k-ANNIHILATING IDEAL HYPERGRAPH OF COMMUTATIVE RINGS

  • Shaymaa S. Essa (Department of Mathematics Duhok University) ;
  • Husam Q. Mohammad (Department of Mathematics Mosul University)
  • Received : 2021.12.21
  • Accepted : 2022.06.15
  • Published : 2023.01.31
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Abstract

In this paper we obtain a new structure of a k-annihilating ideal hypergraph of a reduced ring R, by determine the order and size of a hypergraph 𝒜𝒢k(R). Also we describe and count the degree of every nontrivial ideal of a ring R containing in vertex set 𝒜(R, k) of a hypergraph 𝒜𝒢k(R). Furthermore, we prove the diameter of 𝒜𝒢k(R) must be less than or equal to 2. Finally, we determine the minimal dominating set of a k-annihilating ideal hypergraph of a ring R.

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References

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