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Golbasi, Oznur; Oguz, Seda
Communications of the Korean Mathematical Society, 01/2012, Volume: 27, Issue: 3Journal Article
Let R be a prime ring with center Z and characteristic different from two, U a nonzero Lie ideal of R such that $u^2{\in}U$ for all $u{\in}U$ and $d$ be a nonzero (${\sigma}$, ${\tau}$)-derivation of R. We prove the following results: (i) If $d(u),u_{{\sigma},{\tau}}$ = 0 or $d(u),u_{{\sigma},{\tau}}{\in}C_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$. (ii) If $a{\in}R$ and $d(u),a_{{\sigma},{\tau}}$ = 0 for all $u{\in}U$, then $U{\subseteq}Z$ or $a{\in}Z$. (iii) If $d(u,v)={\pm}u,v_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$. KCI Citation Count: 0
