On weakly (1,n)-ideals and weakly n-ideals

ERSOY B. A., KOÇ S., TEKİR Ü., YEŞİLOT G., YILDIZ YILMAZ E.

Czechoslovak Mathematical Journal, cilt.75, sa.2, ss.611-628, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 75 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.21136/cmj.2025.0337-24
  • Dergi Adı: Czechoslovak Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.611-628
  • Anahtar Kelimeler: 1-absorbing primary ideal, 13A15, n-ideal, weakly (1, n)-ideal, weakly n-ideal
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

We study weakly (1, n)-ideals and weakly n-ideals in commutative rings. Let A be a commutative ring with a nonzero identity and I be a proper ideal of A. Then I is said to be a weakly (1, n)-ideal (or weakly n-ideal) if whenever 0 ≠ abc ∈ I for some nonunits a,b,c ∈ A (or 0 ≠ ab ∈ I for some a,b ∈ A), then either ab ∈ I or c∈N(A) (or a ∈ I or b∈N(A), respectively), where N(A) is the set of all nilpotent elements of A. Many examples and properties of weakly (1, n)-ideals and weakly n-ideals are given. We characterize all rings in which every proper ideal is a weakly (1, n)-ideal and weakly n-ideal. Furthermore, we investigate both weakly (1, n)-ideals and weakly n-ideals in amalgamated algebras along an ideal.