Actions of generalized derivations in Rings and Banach Algebras

摘要

We investigate the action of generalized derivation δ associated with a derivation a in a prime ring R satisfying (i) δ(u)~m - (u)~n ∈ Z(R), for all u ∈ L, a noncentral Lie ideal of R (ii) [δ(x), α(y)]_m=δ([x, y])~n, for all x, y ∈ J, a nonzero ideal of R, where m, n are fixed positive integers. Moreover, we also examine the case when R is semiprime ring. Finally as an application, we obtain some range inclusion results of continuous generalized derivations on Banach algebra 21.