On $S$-$(delta, 2)$-primary ideals of a commutative ring

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Bakkarı C., Hachache R., Koç S., Mahdou N., Tekir Ü., Leoreanu-Fotea V.

CZECHOSLOVAK MATHEMATICAL JOURNAL, cilt.2026, ss.1-16, 2026 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 2026
• Basım Tarihi: 2026
• Doi Numarası: 10.21136/cmj.2026.0349-25
• Dergi Adı: CZECHOSLOVAK MATHEMATICAL JOURNAL
• Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH, DIALNET
• Sayfa Sayıları: ss.1-16
• Marmara Üniversitesi Adresli: Evet

Özet

Let R be a commutative ring with identity, S be a multiplicative set of R,

Id(R) be the set of all ideals of R, and δ : Id(R) → Id(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. We introduce

the concept of S-(δ, 2)-primary ideal which is a generalization of (δ, 2)-primary ideal. Let P

be a proper ideal of R disjoint with S. We say that P is an S-(δ, 2)-primary ideal of R if

there exists s ∈ S such that for all a, b ∈ R, if ab ∈ P , then sa ∈ P or sb ∈ δ(P ). We

next study the possible transfer of the above ideal property to the direct product of rings,

quotient rings, localizations, trivial ring extensions, and amalgamation rings along an ideal