Let $R$ be a non-commutative ring of characteristic different from $2$, with center $Z(R)$, Utumi quotient ring $U$ and extended centroid $C$. Let $G$ be a non-zero generalized derivation of $R$, $L$ be a non-central Lie ideal of $R$, $a$ be an element of $R$. If $aG(u)u=0$, for all $u\in L$, then either $a=0$ or $G(x)=bx$, for all $x\in R$ and $ab=0$.
Generalized Derivations and Annihilator Conditions in Prime Rings
RANIA F
2008-01-01
Abstract
Let $R$ be a non-commutative ring of characteristic different from $2$, with center $Z(R)$, Utumi quotient ring $U$ and extended centroid $C$. Let $G$ be a non-zero generalized derivation of $R$, $L$ be a non-central Lie ideal of $R$, $a$ be an element of $R$. If $aG(u)u=0$, for all $u\in L$, then either $a=0$ or $G(x)=bx$, for all $x\in R$ and $ab=0$.File in questo prodotto:
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