On The Identity d(x) = λx + ζ(x)


The main purpose of this paper is to study and investigate some results concerning generalized derivation D on semiprime ring R, where d a derivation on R and R has a cancellation property with identity. Then under certain conditions we prove that there exist λ C and an additive mapping ζ: R →C such that d(x) = λx + ζ(x) for all x R. Mathematics Subject Classification: 16W25, 16N60, 16U80.