Author/Authors :
Rehman, Nadeem ur Department of mathematics, Aligarh Muslim University, Aligarh, India , Huang, Shuliang School of Mathematics and Finance - Chuzhou University, Chuzhou, Anhui Province, P.R.China , Raza, Mohd Arif Department of Mathematics - Faculty of Science and Arts-Rabigh - King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
Abstract :
Let R be a prime ring with U the Utumi quotient ring and Q be the Martindale quotient ring of R, respectively. Let d be a derivation of R and m,n be fixed positive integers. In this paper, we study the case when one of the following holds:
(i)~ d(x)∘nd(y)=x∘my (ii)~d(x)∘md(y)=(d(x∘y))n for all x,y in some appropriate subset of R. We also examine the case where R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on Banach algebras.
Keywords :
Radical , Banach algebras , Martindale ring of quotients , Derivations , Prime and semiprime rings
