带有广义导子的*-素环上的*-Jordan理想

摘要

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)]=(u o v);(iii)[d(u),F(v)]=uv;(iv)d(u)o F(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F2(u)+ 3d2 (u)=2Fd(u)+ 2dF(u),u∈J,则J(∈)Z(R).