On the nilpotence of the prime radical in module categories

• Date: 2022
• Main Authors: Arellano, C., Castro, J., Ríos, J.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: prime modules; semiprime modules; Goldie modules; torsion theory; nilpotent ideal; nilpotence; 06F25; 16S90; 16D50; 16P50; 16P70
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1634
• Journal Title: Algebra and Discrete Mathematics

For \(M\in R\)-Mod and \(\tau\) a hereditary torsion theory on the category \(\sigma [M]\) we use the concept of prime and semiprime module defined by Raggi et al. to introduce the concept of \(\tau\)-pure prime radical \(\mathfrak{N}_{\tau}(M) =\mathfrak{N}_{\tau}\) as the intersection of all \(\ta...