# A NOTE ON SKEW DERIVATIONS IN PRIME RINGS

De Filippis, Vincenzo;Fosner, Ajda

• Published : 2012.07.31
• 25 3

#### Abstract

Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : $R{\rightarrow}R$ be a skew derivation of R and $E(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)$. We prove that if $E(x)=0$ for all $x{\in}L$, then D is a usual derivation of R or R satisfies $s_4(x_1,{\ldots},x_4)$, the standard identity of degree 4.

#### Keywords

skew derivation;automorphism;prime ring

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