Generalization of ρ-ideals associated with an m-system and a special radical class

ÇAY H., Abouhalaka A., ERSOY B. A.

Ricerche di Matematica, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s11587-024-00912-2
  • Dergi Adı: Ricerche di Matematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: 16N20, 16N40, 16N60, 16N80, 16W99, m-system, Noncommutative ring, prime ideal, S-prime ideal, Special radical classes
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Let ϕ≠S⊆R be an m-system of a ring R, and let ρ be a special radical. This study introduces the concept of S-ρ-ideals in noncommutative rings. This notion extends the previously studied ρ-ideals and can also be seen as a generalization of the right S-prime ideals. We show how some properties associated with ρ-ideals have evolved into results within these generalizations. Relationships between S-ρ-ideals and other types of ideals like ρ-ideals, right S-prime ideals, and S-finite ideals are shown. We show the behaviour of this notion in related rings. The construction of (S⊞M)-ρ-ideals in idealization rings is presented for an R-R-bimodule M. Additionally, we introduce S-P-ideals using Baer-McCoy radical P and examine their properties.