NOTES ON (σ, τ)-DERIVATIONS OF LIE IDEALS IN PRIME RINGS

OpenAlex · İngilizce

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 $U{\subseteq}Z$ .