TY - JOUR ID - 97174 TI - On Pair of Generalized Derivations in Rings JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Ali, Asma AU - Rahaman, Md Hamidur AD - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. Y1 - 2020 PY - 2020 VL - 6 IS - 1 SP - 87 EP - 94 KW - Prime rings KW - semiprime rings KW - generalized derivations KW - extended centroid DO - 10.22034/kjm.2019.97174 N2 - 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 $R$. UR - https://www.kjm-math.org/article_97174.html L1 - https://www.kjm-math.org/article_97174_d6600441ebda02c760dafc2171b8c9a6.pdf ER -