-CENTRALIZING MAPPINGS OF SEMIPRIME -RINGS
Let M be a -Ring with center Z(M) and S a non-empty subset of M. A mapping F from M to M is called -centralizing on S if [x,F(x)]α= xαF(x)-F(x)αxZ(M) for all xS,α . 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.