@article{Pehlivan_Albaş_2022, title={$b$ -Generalized derivations on prime rings}, volume={74}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/5989}, DOI={10.37863/umzh.v74i6.5989}, abstractNote={<p>Let $R$ be a prime ring with center $Z(R)$, right Martindale quotient ring $Q$ and extended centroid $C$. By a $b$-generalized derivation we mean an additive mapping $g:R\rightarrow Q$ such that $g(xy) = g(x)y + bxd(y)$ for all $x,y \in R$, where $b \in Q$ and $d: R \rightarrow Q$ is an additive map. In this paper, we extend some well-known results concerning (generalized) derivations on prime rings to $b$-generalized derivations. Further we investigate $b$-generalized derivation acting as a homomorphism or anti-homomorphism in a prime ring.</p>}, number={6}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Pehlivan, T. and Albaş, E.}, year={2022}, month={Jul.}, pages={832 - 843} }