On a subset with nilpotent values in a prime ring with derivation
De Filippis, Vincenzo
Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 833-838 / Harvested from Biblioteca Digitale Italiana di Matematica
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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∈I, there exists n=n⁢x,y≥1 such that d⁢x,y-x,yn=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∈I, esiste n=n⁢x,y≥1 tale che d⁢x,y-x,yn=0 , allora R é commutativo. Come conseguenza si ottiene una estensione di tale risultato per ideali di Lie di R.

Publié le : 2002-10-01
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     author = {Vincenzo De Filippis},
     title = {On a subset with nilpotent values in a prime ring with derivation},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5-A},
     year = {2002},
     pages = {833-838},
     zbl = {1119.16035},
     mrnumber = {1934384},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_3_833_0}
}

De Filippis, Vincenzo. On a subset with nilpotent values in a prime ring with derivation. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 833-838. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_3_833_0/

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