TY - JOUR
T1 - Left Annihilator of Identities Involving Generalized Derivations in Prime Rings
JF - IJMSI
JO - IJMSI
VL - 12
IS - 2
UR - http://ijmsi.ir/article-1-845-en.html
Y1 - 2017
SP - 141
EP - 153
KW Prime ring
KW Generalized derivation
KW Utumi quotient ring.
N2 - Let $R$ be a prime ring with its Utumi ring of quotients $U$, $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$ and $0neq a in R$. If $R$ admits a generalized derivation $F$ such that $a(F(u^2)pm F(u)^{2})=0$ for all $u in L$, then one of the following holds: begin{enumerate} item there exists $b in U$ such that $F(x)=bx$ for all $x in R$, with $ab=0$; item $F(x)=mp x$ for all $x in R$; item char $(R)=2$ and $R$ satisfies $s_4$;item char $(R) neq 2$, $R$ satisfies $s_4$ and there exists $bin U$ such that $F(x)=bx$ for all $x in R$.
M3 10.7508/ijmsi.2017.2.010
ER -