S-Weakly Prime Ideals in Noncommutative Rings

ÇAY H., ERSOY B. A.

Ukrainian Mathematical Journal, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s11253-025-02493-1
  • Dergi Adı: Ukrainian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Let R be a noncommutative ring. The works by Hirano et al. and Groenewald (see [Bull. Korean Math. Soc., 47, No. 5, 1077–1087 (2010)] and [Int. Electron. J. Algebra, 28, 43–68 (2020)]), were devoted to the investigation of weakly prime ideals in noncommutative rings. In this work, we generalize their findings by introducing the concept of S-weakly prime ideals via taking S as an m-system, which is also a generalization of the concept of right S-prime ideals first introduced in [Mediterran. J. Math., 21, No. 2, Article 43 (2024)].