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.

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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.
Siano $R$ un anello primo, privo di nil ideali destri, $d$ una derivazione non nulla di $R$, $I$ un ideale bilatero non nullo di $R$. Se, per ogni $x$, $y \in I$, esiste $n= n(x, y)\geq 1$ tale che $( d ([x, y]) - [x, y] )^{n}=0$ , allora $R$ é commutativo. Come conseguenza si ottiene una estensione di tale risultato per ideali di Lie di $R$. 
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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/

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