On 1-absorbing delta-primary ideals

El Khalfi A., Mahdou N., Tekir Ü., Koç S.

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica, cilt.29, sa.3, ss.1-16, 2021 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 3
  • Basım Tarihi: 2021
  • Dergi Adı: Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1-16
  • Marmara Üniversitesi Adresli: Evet

Özet

Let R be a commutative ring with nonzero identity. Let I(R) be the set of all ideals of R and let 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). Let δ be an expansion function of ideals of R. In this paper, we introduce and investigate a new class of ideals that is closely related to the class of δ-primary ideals. A proper ideal I of R is said to be a 1-absorbing δ-primary ideal if whenever nonunit elements a, b, c ∈ R and abc ∈ I, then ab ∈ I or c ∈ δ(I). Moreover, we give some basic properties of this class of ideals and we study the 1-absorbing δ-primary ideals of the localization of rings, the direct product of rings and the trivial ring extensions.