Modules which have a rad-supplement that is a direct summand in every extension
In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular, we prove that a semisimple module \(M\) is \(\operatorname{Rad}\)-supplementing if and only if \(M\) has the property (SRE). Moreover, we show tha...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/159 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular, we prove that a semisimple module \(M\) is \(\operatorname{Rad}\)-supplementing if and only if \(M\) has the property (SRE). Moreover, we show that a ring \(R\) is a left V-ring if and only if every left \(R\)-module with the property (RE) is injective. Finally, we characterize the rings whose modules have the properties (RE) and (SRE). |
|---|