An identity with derivations in prime rings
Let R be a prime ring with center Z(R), and d a derivation of R. Suppose that (d[x, y]k)n - m[x, y]k ∈ Z(R) for all x,y ∈ R, where m ≠ n,k ≥ 1 are fixed integers. Then d = 0 or R satisfies s4, the standard identity in four variables. In the case (d[x,y]k)n - m[x, y]k = 0 for all x,y ∈ R, then d = 0...
Gespeichert in:
| Veröffentlicht in: | Mathematical notes (Miskolci Egyetem (Hungary)) 2018, Vol.19 (2), p.899-905 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | Let R be a prime ring with center Z(R), and d a derivation of R. Suppose that (d[x, y]k)n - m[x, y]k ∈ Z(R) for all x,y ∈ R, where m ≠ n,k ≥ 1 are fixed integers. Then d = 0 or R satisfies s4, the standard identity in four variables. In the case (d[x,y]k)n - m[x, y]k = 0 for all x,y ∈ R, then d = 0 or R is commutative. |
|---|---|
| ISSN: | 1787-2405 1787-2413 |
| DOI: | 10.18514/MMN.2018.1529 |