an:01537816
Zbl 1009.16034
Carini, Luisa; De Filippis, Vincenzo
Commutators with power central values on a Lie ideal
EN
Pac. J. Math. 193, No. 2, 269-278 (2000).
00072057
2000
j
16W10 16N60 16R50
prime rings; derivations; Lie ideals; semiprime rings; commutators
Summary: Let \(R\) be a prime ring of characteristic \(\neq 2\) with a derivation \(d\neq 0\), \(L\) a noncentral Lie ideal of \(R\) such that \([d(u),u]^n\) is central, for all \(u\in L\). We prove that \(R\) must satisfy \(s_4\), the standard identity in \(4\) variables. We also examine the case \(R\) is a 2-torsion free semiprime ring and \([d([x,y]),[x,y]]^n\) is central, for all \(x,y\in R\).