Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON WEAKLY (m, n)-PRIME IDEALS OF COMMUTATIVE RINGS

  • 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 : 2023.05.24
  • Accepted : 2023.08.25
  • Published : 2024.05.31
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Abstract

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of weakly (m, n)-prime ideals generalizing (m, n)-prime and weakly (m, n)-closed ideals. A proper ideal I of R is called weakly (m, n)-prime if for a, b ∈ R, 0 ≠ amb ∈ I implies either an ∈ I or b ∈ I. We justify several properties and characterizations of weakly (m, n)-prime ideals with many supporting examples. Furthermore, we investigate weakly (m, n)-prime ideals under various contexts of constructions such as direct products, localizations and homomorphic images. Finally, we discuss the behaviour of this class of ideals in idealization and amalgamated rings.

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References

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