Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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(m, n)-CLOSED δ-PRIMARY IDEALS IN AMALGAMATION

  • Mohammad Hamoda (Department of Mathematics Faculty of Applied Science Al-Aqsa University) ;
  • Mohammed Issoual (Departement of Mathematics CRMEF Rabat-Sale-Kenitra)
  • Received : 2023.10.08
  • Accepted : 2024.02.29
  • Published : 2024.07.31
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Abstract

Let R be a commutative ring with 1 ≠ 0. Let Id(R) be the set of all ideals of R and let δ : Id(R) → Id(R) be a function. Then δ is called an expansion function of the ideals of R if whenever L, I, J are ideals of R with J ⊆ I, then L ⊆ δ (L) and δ (J) ⊆ δ (I). Let δ be an expansion function of the ideals of R and m ≥ n > 0 be positive integers. Then a proper ideal I of R is called an (m, n)-closed δ-primary ideal (resp., weakly (m, n)-closed δ-primary ideal ) if am ∈ I for some a ∈ R implies an ∈ δ(I) (resp., if 0 ≠ am ∈ I for some a ∈ R implies an ∈ δ(I)). Let f : A → B be a ring homomorphism and let J be an ideal of B. This paper investigates the concept of (m, n)-closed δ-primary ideals in the amalgamation of A with B along J with respect to f denoted by A ⋈f J.

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References

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