Two Results on Square Closed Lie Ideals of Prime Rings

Abstract:

      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 $U\subseteq Z(R)$.