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ISSN : 1226-0657

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Vol.23 No.4

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JORDAN DERIVATIONS ON A LIE IDEAL OF A SEMIPRIME RING AND THEIR APPLICATIONS IN BANACH ALGEBRAS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2016, v.23 no.4, pp.347-375
https://doi.org/10.7468/jksmeb.2016.23.4.347
Kim, Byung-Do
Kim,, B. (2016). JORDAN DERIVATIONS ON A LIE IDEAL OF A SEMIPRIME RING AND THEIR APPLICATIONS IN BANACH ALGEBRAS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(4), 347-375, https://doi.org/10.7468/jksmeb.2016.23.4.347

Abstract

Let R be a 3!-torsion free noncommutative semiprime ring, U a Lie ideal of R, and let <TEX>$D:R{\rightarrow}R$</TEX> be a Jordan derivation. If [D(x), x]D(x) = 0 for all <TEX>$x{\in}U$</TEX>, then D(x)[D(x), x]y - yD(x)[D(x), x] = 0 for all <TEX>$x,y{\in}U$</TEX>. And also, if D(x)[D(x), x] = 0 for all <TEX>$x{\in}U$</TEX>, then [D(x), x]D(x)y - y[D(x), x]D(x) = 0 for all <TEX>$x,y{\in}U$</TEX>. And we shall give their applications in Banach algebras.

keywords
Banach algebra, (Jacobson) radical, derivation, Jordan derivation, Lie ideal, prime ring, semiprime ring

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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