A NOTE ON LIE IDEALS OF PRIME RINGS

Title & Authors
A NOTE ON LIE IDEALS OF PRIME RINGS
Shuliang, Huang;

Abstract
Let R be a 2-torsion free prime ring, U a nonzero Lie ideal of R such that $\small{u^2\;{\in}\;U}$ for all $\small{u\;{\in}\;U}$. In the present paper, it is proved that if d is a nonzero derivation and [[d(u), u], u] = 0 for all $\small{u\;{\in}\;U}$, then $\small{U\;{\subseteq}\;Z(R)}$. Moreover, suppose that $\small{d_1}$, $\small{d_2}$, $\small{d_3}$ are nonzero derivations of R such that $\small{d_3(y)d_1(x)\;=\;d_2(x)d_3(y)}$ for all x, $\small{y\;{\in}\;U}$, then $\small{U\;{\subseteq}\;Z(R)}$. Finally, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the above results are not superfluous.
Keywords
prime ring;derivation;Lie ideal;
Language
English
Cited by
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