Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GENERALIZATIONS OF 2-ABSORBING PRINCIPALLY RIGHT PRIMARY IDEALS IN NON-COMMUTATIVE RINGS

  • Nico J. Groenewald (Department of Mathematics Nelson Mandela University) ;
  • Ece Yetkin Celikel (Department of Software Engineering Hasan Kalyoncu University)
  • Received : 2024.06.11
  • Accepted : 2025.05.21
  • Published : 2025.10.31
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Abstract

Let R be a non-commutative ring with 1 ≠ 0 and S(R) be the set of all ideals of R. In this paper, we extend the concept of 2-absorbing principally right primary ideals to the context of 𝜙-2-absorbing principally right primary ideals. Let 𝜙 : S(R) → S(R) ∪ {Ø} be a function. A proper ideal I of R is said to be a 𝜙-2-absorbing principally right primary ideal of R if whenever a, b, c ∈ R with aRbRc ⊆ I and aRbRc ⊈ 𝜙(I) implies ab ∈ I or ac ∈ $\sqrt{I}$ or bc ∈ $\sqrt{I}$. A number of results and characterizations concerning 𝜙-2-absorbing principally right primary ideals are given.

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References

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