Let $R$ be an associative ring with extended centroid $C$, let $G$ and $F$ be generalized derivations of $R$ associated with nonzero derivations $\delta$ and $d$, respectively, and let $m, k, n \geq1$ be fixed integers. In the present paper, we study the situations: (i)$F(x)\circ_{m}G(y)=(x \circ_{n} y)^{k}$, (ii) $[F(x),y]_{m}+[x,d(y)]_{n}=0$ for all $y, x$ in some appropriate subset of $R$.
Ali, A., & Rahaman, M. (2020). On Pair of Generalized Derivations in Rings. Khayyam Journal of Mathematics, 6(1), 87-94. doi: 10.22034/kjm.2019.97174
MLA
Asma Ali; Md Hamidur Rahaman. "On Pair of Generalized Derivations in Rings". Khayyam Journal of Mathematics, 6, 1, 2020, 87-94. doi: 10.22034/kjm.2019.97174
HARVARD
Ali, A., Rahaman, M. (2020). 'On Pair of Generalized Derivations in Rings', Khayyam Journal of Mathematics, 6(1), pp. 87-94. doi: 10.22034/kjm.2019.97174
VANCOUVER
Ali, A., Rahaman, M. On Pair of Generalized Derivations in Rings. Khayyam Journal of Mathematics, 2020; 6(1): 87-94. doi: 10.22034/kjm.2019.97174