ON n-CENTRALIZING GENERALIZED DERIVATIONS IN SEMIPRIME RINGS WITH APPLICATIONS TO C*-ALGEBRAS

Let R be a ring with center Z(R) and n be a fixed positive integer. A mapping f : R -> R is said to be n-centralizing on a subset S of R if f(x)x(n) -x(n)f(x). Z(R) holds for all x is an element of S. The main result of this paper states that every n-centralizing generalized derivation F on a (n+1)!-torsion free semiprime ring is n-commuting. Further, we prove that if a generalized derivation F : R -> R is n-centralizing on a nonzero left ideal lambda, then either R contains a nonzero central ideal or lambda D(Z) subset of Z(R) for some derivation D of R. As an application, n-centralizing generalized derivations of C*-algebras are characterized.