On a subset with nilpotent values in a prime ring with derivation
Bollettino dell'Unione Matematica Italiana (2002)
- Volume: 5-B, Issue: 3, page 833-838
- ISSN: 0392-4041
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topDe Filippis, Vincenzo. "On a subset with nilpotent values in a prime ring with derivation." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 833-838. <http://eudml.org/doc/195233>.
@article{DeFilippis2002,
abstract = {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.},
author = {De Filippis, Vincenzo},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {derivations with nilpotent values; prime rings; commutativity theorems; Lie ideals},
language = {eng},
month = {10},
number = {3},
pages = {833-838},
publisher = {Unione Matematica Italiana},
title = {On a subset with nilpotent values in a prime ring with derivation},
url = {http://eudml.org/doc/195233},
volume = {5-B},
year = {2002},
}
TY - JOUR
AU - De Filippis, Vincenzo
TI - On a subset with nilpotent values in a prime ring with derivation
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 833
EP - 838
AB - 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.
LA - eng
KW - derivations with nilpotent values; prime rings; commutativity theorems; Lie ideals
UR - http://eudml.org/doc/195233
ER -
References
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