关于素环平方封闭的李理想的两个结果

Let R be a 2-torsion free prime ring, d1 a nonzero derivation, -γ a generalized derivation associated with a nonzero derivation d2, U a square closed Lie ideal of R. In the present paper,we prove that if di^2（u）, u] ∈ Z（R） or γ acts as a homomorphism （or an antihomomorphism） on U, then U Z（R）.

Two Results on Square Closed Lie Ideals of Prime Rings

Let $R$ be a $2$-torsion free prime ring, $d_{1}$ a nonzero derivation, $\gamma$ a generalized derivation associated with a nonzero derivation $d_{2}$, $U$ a square closed Lie ideal of $R$. In the present paper, we prove that if $d_{1}^{2}(u),u]\in Z(R)$ or $\gamma$ acts as a homomorphism (or an antihomomorphism) on $U$, then $U\subseteq Z(R)$.