Generalized Left Jordan ideals In Prime Rings

Abstract

     Let R be a prime ring and U be a (σ,τ)-left Jordan ideal .Then in this paper, we proved the following , if aU Z (Ua Z), a R, then a = 0 or U Z. If aU C _s,t (Ua  C _s,t), a R, then  either a = 0   or   U Z. If  0 ≠ [U,U] _s,t .Then U Z. If  0≠[U,U] _s,t C _s,t, then   U Z  .Also, we checked the converse  some of these theorems and showed that are not true, so we give an example for them.