Geodesic
On a subset with nilpotent values in a prime ring with derivation
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 833-838

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Let $R$ be a prime ring, with no non-zero nil right ideal, $d$ a non-zero drivation of $R$, $I$ a non-zero two-sided ideal of $R$. If, for any $x$, $y \in I$, there exists $n= n(x, y)\geq 1$ such that $( d ([x, y]) - [x, y] )^{n}=0$, then $R$ is commutative. As a consequence we extend the result to Lie ideals. 
@article{BUMI_2002_8_5B_3_a16,
     author = {De Filippis, Vincenzo},
     title = {On a subset with nilpotent values in a prime ring with derivation},
     journal = {Bollettino della Unione matematica italiana},
     pages = {833--838},
     publisher = {mathdoc},
     volume = {Ser. 8, 5B},
     number = {3},
     year = {2002},
     zbl = {1119.16035},
     mrnumber = {MR1934384},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_3_a16/}
}
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De Filippis, Vincenzo. On a subset with nilpotent values in a prime ring with derivation. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 833-838. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_3_a16/