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Korean Mathematical Society (대한수학회)
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THE PROPERTIES OF JORDAN DERIVATIONS OF SEMIPRIME RINGS AND BANACH ALGEBRAS, I

  • Kim, Byung Do (Department of Mathematics Gangneung-Wonju National University)
  • Received : 2016.07.27
  • Accepted : 2017.08.09
  • Published : 2018.01.31
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Abstract

Let R be a 5!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. Then $[D(x),x]D(x)^2=0$ if and only if $D(x)^2[D(x), x]=0$ for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A) and if D is a continuous linear Jordan derivation on A, then we show that $[D(x),x]D(x)2{\in}rad(A)$ if and only if $D(x)^2[D(x),x]{\in}rad(A)$ for all $x{\in}A$ where rad(A) is the Jacobson radical of A.

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References

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