Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE RESULTS CONCERNING JORDAN DERIVATIONS

  • Kim, Byung Do (Department of Mathematics Gangneung-Wonju National University)
  • Received : 2016.03.10
  • Accepted : 2016.10.17
  • Published : 2016.11.15
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Abstract

Let R be a 3!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. In this case, we show that [D(x), x]D(x) = 0 if and only if D(x)[D(x), x] = 0 for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A). If D is a continuous linear Jordan derivation on A, then we see that $[D(x),x]D(x){\in}rad(A)$ if and only if $[D(x),x]D(x){\in}rad(A)$ for all $x{\in}A$.

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References

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