半素环的中心自同态

THE CENTRALISING ENDOMORPHISM OF SEMIPRIME RINGS

证明了如下定理：设Ｒ是半承环，Ｕ为Ｒ的１个非零左理想，若Ｒ容许１个满自同态Ｔ使得Ｔ在Ｕ上是中心的，而Ｖ＝Ｕ￣Ｔ￣（－１）－∩Ｕ∩Ｕ￣Ｔ≠｛０｝且Ｔ在ｖ上不是恒等映射，则Ｒ含有非零的中心理想。

he following result is proved:Let R be a semiprime ring and U be a nonzero left idealof R,Suppose that R admits an epimorphism T of R,such that T is centralising on U,V=and T is not identical on V,then R contains nonzero central ideal.