Generalization of ρ-ideals associated with an m-system and a special radical class
Ricerche di Matematica, cilt.74, sa.3, ss.1467-1482, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 74 Sayı: 3
- Basım Tarihi: 2025
- 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
- Sayfa Sayıları: ss.1467-1482
- Anahtar Kelimeler: 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.