带有广义导子的~*-素环上的~*-Jordan理想

On Jordan Ideals of *-Prime Rings with Generalized Derivations

R是2-扭自由*-素环,J是R的非零*-Jordan理想。F是R的广义导子,其非零伴随导子d与*可交换,对u,v∈J有(i)d(u)oF(v)=[u,v];(ii)[d(u),F(v)]=(uov);(iii)[d(u),F(v)]=uv;(iv)d(u)oF(v)=uv;(v)d(u)F(v)=[u,v];(vi)d(u)F(v)=uov。若F=0或d≠0,则J■Z(R);(vii)若F^2(u)(10)3d^2(u)=2Fd(u)+2d F(u),u∈J,则J■Z(R)。

In the present paper, it is shown that： if R is 2-torsion free ^＊-prime ring, J be a nonzero^＊-Jordan ideal. F is called a generalized derivation associated with a derivation d. There exists follows： （i） d（u）oF（v）=[u,v];（ii）[d（u）,F（v）]=（uov）;（iii）[d（u）,F（v）]=uv;（iv）d（u）oF（v）=uv;（v）d（u）F（v）=[u,v];（vi）d（u）F（v）=uov.IfF=0ord≠0,then J Z（R）; （vii）If F^2（u）＋3d^2（u）=2Fd（u）,u∈J,then J Z（R）