Let I be a *-ideal on a 2-torsion free *-prime ring and F : R → R a generalized derivation with an associated derivation d : R → R. The aim of this paper is to explore the condition under which generalized derivation F becomes a left centralizer i.e., associated derivation d becomes a trivial map (i.e., zero map) on R.

Keywords: derivation, generalized derivation, *-prime ring, centralizer.