대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제49권4호
  • /
  • Pages.885-898
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  • 2012
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A NOTE ON SKEW DERIVATIONS IN PRIME RINGS

  • 투고 : 2011.04.28
  • 발행 : 2012.07.31
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초록

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.

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참고문헌

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