On the nilpotence of the prime radical in module categories
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...
Gespeichert in:
| Datum: | 2022 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2022
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1634 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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 \(\tau\)-pure prime submodules of \(M\). We give necessary and sufficient conditions for the \(\tau\)-nilpotence of \(\mathfrak{N}_{\tau}(M) \). We prove that if \(M\) is a finitely generated \(R\)-module, progenerator in \(\sigma [M]\) and \(\chi\neq \tau\) is FIS-invariant torsion theory such that \(M\) has \(\tau\)-Krull dimension, then \(\mathfrak{N}_{\tau}\) is \(\tau\)-nilpotent. |
|---|