δ(0)-IDEALS OF COMMUTATIVE RINGS

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Chhiti M., ERSOY B. A., Kaiba K., TEKİR Ü.

International Electronic Journal of Algebra, vol.36, no.36, pp.16-28, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 36
  • Publication Date: 2024
  • Doi Number: 10.24330/ieja.1438744
  • Journal Name: International Electronic Journal of Algebra
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.16-28
  • Keywords: n-ideal, Prime ideal, trivial ring extension, δ(0)-ideal, δ-primary ideal
  • Yıldız Technical University Affiliated: Yes

Abstract

Let R be a commutative ring with nonzero identity, let I(R) be the set of all ideals of R and δ: I(R) → I(R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J ⊆ I, we have L ⊆ δ(L) and δ(J) ⊆ δ(I). In this paper, we present the concept of δ(0)-ideals in commutative rings. A proper ideal I of R is called a δ(0)-ideal if whenever a, b ∈ R with ab ∈ I and a ∉ δ(0), we have b ∈ I. Our purpose is to extend the concept of n-ideals to δ(0)-ideals of commutative rings. Then we investigate the basic properties of δ(0)-ideals and also, we give many examples about δ(0)-ideals.