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

Title & Authors
NOTES ON (σ, τ)-DERIVATIONS OF LIE IDEALS IN PRIME RINGS
Golbasi, Oznur; Oguz, Seda;

Abstract
Let R be a prime ring with center Z and characteristic different from two, U a nonzero Lie ideal of R such that $\small{u^2{\in}U}$ for all $\small{u{\in}U}$ and $\small{d}$ be a nonzero ($\small{{\sigma}}$, $\small{{\tau}}$)-derivation of R. We prove the following results: (i) If $\small{[d(u),u]_{{\sigma},{\tau}}}$ = 0 or $\small{[d(u),u]_{{\sigma},{\tau}}{\in}C_{{\sigma},{\tau}}}$ for all $\small{u{\in}U}$, then $\small{U{\subseteq}Z}$. (ii) If $\small{a{\in}R}$ and $\small{[d(u),a]_{{\sigma},{\tau}}}$ = 0 for all $\small{u{\in}U}$, then $\small{U{\subseteq}Z}$ or $\small{a{\in}Z}$. (iii) If $\small{d([u,v])={\pm}[u,v]_{{\sigma},{\tau}}}$ for all $\small{u{\in}U}$, then $\small{U{\subseteq}Z}$.
Keywords
derivations;Lie ideals;($\small{{\sigma}}$, $\small{{\tau}}$)-derivations;centralizing mappings;prime rings;
Language
English
Cited by
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