On sum of a nilpotent and an ideally finite algebras
We study associative algebras \(R\) over arbitrary fields which can be decomposed into a sum \(R=A+B\) of their subalgebras \(A\) and \(B\) such that \(A^{2}=0\) and \(B\) is ideally finite (is a sum of its finite dimensional ideals). We prove that \(R\) has a locally nilpotent ideal \(I\) such tha...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/856 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | We study associative algebras \(R\) over arbitrary fields which can be decomposed into a sum \(R=A+B\) of their subalgebras \(A\) and \(B\) such that \(A^{2}=0\) and \(B\) is ideally finite (is a sum of its finite dimensional ideals). We prove that \(R\) has a locally nilpotent ideal \(I\) such that \(R/I\) is an extension of ideally finite algebra by a nilpotent algebra. Some properties of ideally finite algebras are also established. |
|---|