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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics, Gangneung-Wonju National University)

Kim, Byung-Do. (2016). JORDAN DERIVATIONS ON A LIE IDEAL OF A SEMIPRIME RING AND THEIR APPLICATIONS IN BANACH ALGEBRAS. 한국수학교육학회지시리즈B:순수및응용수학, 23(4), 347-375, https://doi.org/10.7468/jksmeb.2016.23.4.347

복사

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

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Vol.23 No.4

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

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학