Annihilator conditions with generalized skew derivations and Lie ideals of prime rings

Authors : Vincenzo DE FILIPPIS, Nadeem Ur REHMAN, Giovanni SCUDO

Pages : 192-216

Doi:10.24330/ieja.1143810

View : 13 | Download : 9

Publication Date : 2022-07-16

Article Type : Research Paper

Abstract :Let $R$ be a prime ring, $Q_r$ its right Martindale quotient ring, $L$ a non-central Lie ideal of $R$, $n\geq 1$ a fixed integer, $F$ and $G$ two generalized skew derivations of $R$ with the same associated automorphism, $p\in R$ a fixed element. If $p\biglinsert ignore into journalissuearticles values(Finsert ignore into journalissuearticles values(x);Finsert ignore into journalissuearticles values(y);-Ginsert ignore into journalissuearticles values(y);x\bigr);^n=0$, for any $x,y \in L$, then there exist $a,c\in Q_r$ such that $Finsert ignore into journalissuearticles values(x);=ax$ and $Ginsert ignore into journalissuearticles values(x);=cx$, for any $x\in R$, with $pa=pc=0$, unless when $R$ satisfies the standard polynomial identity $s_4insert ignore into journalissuearticles values(x_1,\ldots,x_4);$.
Keywords : Generalized, skew derivation, prime ring