This article is cited in 26 papers

On Lie ideals with generalized derivations

Ö. Gölbaşi^a, K. Kaya<sup>b

a</sup> Cumhuriyet University
^b Çanakkale Onsekiz Mart University

Abstract: Let $R$ be a prime ring with characteristic different from 2, let $U$ be a nonzero Lie ideal of $R$, and let $f$ be a generalized derivation associated with $d$. We prove the following results: (i) If $a\in R$ and $[a,f(U)]=0$ then $a\in Z$ or $d(a)=0$ or $U\subset Z$; (ii) If $f^2(U)=0$ then $U\subset Z$; (iii) If $u^2\in U$ for all $u\in U$ and $f$ acts as a homomorphism or antihomomorphism on $U$ then either $d=0$ or $U\subset Z$.

Keywords: derivation, Lie ideal, generalized derivation, homomorphism, antihomomorphism.

UDC: 512.552.16

Received: 04.02.2005
Revised: 10.01.2006

 English version: Siberian Mathematical Journal, 2006, 47:5, 862–866

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