Γ-CENTRALIZING MAPPINGS OF SEMIPRIME Γ-RINGS

Let M be a Γ-Ring with center Z(M) and S a non-empty subset of M. A mapping F from M to M is called Γ-centralizing on S if [x,F(x)]α= xαF(x)-F(x)αx ϵ Z(M) for all x ϵ S,α ϵ Γ . we show that a semi- prime Γ-ring M must have a non-trivial central ideal if it admits an endomorphism which is Γ- centralizing on some non-trivial one –sided ideal.