A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings
Journal of Mathematics, vol.2024, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2024
- Publication Date: 2024
- Doi Number: 10.1155/2024/9142090
- Journal Name: Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Çukurova University Affiliated: Yes
Abstract
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.