Annihilators of power values of b-generalized derivations in prime rings

Authors : Nihan BAYDAR YARBİL

Pages : 1278-1284

Doi:10.31801/cfsuasmas.628755

View : 18 | Download : 12

Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :Let $R$ be a prime ring with extended centroid $C$ and maximal left ring of quotients $Q_{ml}insert ignore into journalissuearticles values(R);$.  For  a nonzero element $b\in R$ let $F:R\rightarrow R$ be a right generalized $b$-derivation associated with the map $d$ of $R$. Suppose that  $s\leftinsert ignore into journalissuearticles values(Finsert ignore into journalissuearticles values(x);\right);^n=0$ for all $x\in R$ where $s$ is a nonzero element in $R$ and $n\geq 1$ is a fixed positive integer. Then  there exist some $c\in Q{ml}insert ignore into journalissuearticles values(R);$ and $\beta \in C$ such that $dinsert ignore into journalissuearticles values(x);=ad_cinsert ignore into journalissuearticles values(x);$, $Finsert ignore into journalissuearticles values(x);=insert ignore into journalissuearticles values(b+\beta);xb$ for all $x\in R$ and either $sinsert ignore into journalissuearticles values(c+\beta);=0$ or $binsert ignore into journalissuearticles values(c+\beta);=0$.
Keywords : Prime ring, generalized polynomial identity