TY - JOUR
ID - 7528
TI - A note on b-generalized derivations with a quadratic equation in prime rings
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Yılmaz, Damla
AU - Yazarlı, Hasret
AD - Department of Mathematics, Faculty of Science, Erzurum Technical University, Erzurum, Turkey
AD - Department of Mathematics, Faculty of Science, Sivas Cumhuriyet University, Sivas, Turkey
Y1 - 2023
PY - 2023
VL - 14
IS - 5
SP - 199
EP - 209
KW - b-generalized derivation
KW - multilinear polynomial
KW - prime ring
KW - generalized polynomial identity
DO - 10.22075/ijnaa.2023.28801.3994
N2 - Let $R$ be a prime ring of characteristic different from $2$, $C$ be its extended centroid and $Q_{r}$ be its right Martindale quotient ring and $f(t_{1},...,t_{n})$ be a multilinear polynomial over $C$, which is not central valued on $R$. Assume that $F$ is a $b$-generalized derivation on $R$ and $d$ is a derivation of $R$ such that $$ F(f(s))d(f(s))+d(f(s))F(f(s))=0$$for all $s=(s_{1},...,s_{n})\in R^{n}$. Then either $F=0$ or $d=0$, except when $d$ is an inner derivation of $R$, there exists $\lambda \in C$ such that $F(r)=\lambda r$ for all $r\in R$ and $f(t_{1},...,t_{n})^{2}$ is central valued on $R$.
UR - https://ijnaa.semnan.ac.ir/article_7528.html
L1 - https://ijnaa.semnan.ac.ir/article_7528_7ec9b0296ee16f31d4df1ca6067aeab2.pdf
ER -