Two generalized derivations on Lie ideals in prime rings

Authors : Ashutosh PANDEY, Balchand PRAJAPATİ

Pages : 48-61

Doi:10.24330/ieja.1281636

View : 34 | Download : 34

Publication Date : 2023-07-10

Article Type : Research Paper

Abstract :Let $R$ be a prime ring of characteristic not equal to $2$, $U$ be the Utumi quotient ring of $R$ and $C$ be the extended centroid of $R$. Let $G$ and $F$ be two generalized derivations on $R$ and $L$ be a non-central Lie ideal of $R$. If $F\\Biginsert ignore into journalissuearticles values(Ginsert ignore into journalissuearticles values(u);\\Big);u = Ginsert ignore into journalissuearticles values(u^{2});$ for all $u \\in L$, then one of the following holds: insert ignore into journalissuearticles values(1); $G=0$. insert ignore into journalissuearticles values(2); There exist $p,q \\in U$ such that $Ginsert ignore into journalissuearticles values(x);=p x$, $Finsert ignore into journalissuearticles values(x);=qx$ for all $x \\in R$ with $qp=p$. insert ignore into journalissuearticles values(3); $R$ satisfies $s_4$.
Keywords : Lie ideal, generalized derivation, extended centroid, Utumi quotient ring