A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings

Alaa Abouhalaka and Francesca Tartarone

Journal of Mathematics, 2024, vol. 2024, 1-6

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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9142090

DOI: 10.1155/2024/9142090

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