广义导子在素环李理想上的作用

摘要

Let R be a prime ring with charR≠2, U(∈)Z(R) a Lie ideal such that u2∈U for all u∈U, and δ a generalized derivation associated with d.If either δ(U)(∈)Z(R) or［δ(x),δ(y)=x,y］ with d(Z(U))≠0 for all x, y∈U, then there exists q∈Qr(Rc) such that δ(x)=qx for all x∈R. Further, if a∈R and ［a,δ(x)］∈Z(R) with d(Z(U))≠0 for all x∈U, then a∈Z(R).%设R是特征不为2的素环,U是平方封闭的非中心李理想,δ是伴随为d的广义导子,如果有δ(U)(∈)Z(R)或[δ(x),δ(y)]=[x,y]并满足 d(Z(U))≠0,那么存在q∈Qr(Rc)使得对所有的x∈R,有δ(x)=qx.此外,如果对于所有x∈U, [a,δ(x)]∈Z(R) 并满足d(Z(U))≠0,那么a∈Z(R).