A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings
Journal of Mathematics, cilt.2024, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2024
- Basım Tarihi: 2024
- Doi Numarası: 10.1155/2024/9142090
- Dergi Adı: Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Çukurova Üniversitesi Adresli: Evet
Özet
In this paper, we introduce the concept of weakly semiprime ideals and weakly n-systems in noncommutative rings. We establish the equivalence between an ideal P being a weakly semiprime ideal and R-P being a weakly n-system. We provide alternative definitions and explore the properties of weakly semiprime ideals. Additionally, we investigate scenarios where all ideals in a given ring are weakly semiprime and demonstrate that in Noetherian rings, where every ideal is weakly semiprime, the prime radical and the Jacobson radical coincide.