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Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that $D^2(x)[D(x),x]=0$ or $[D(x),x]D^2(x)=0$ for all $x{\in}R$. In this case we have $f(x)^5=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $D^2(x)[D(x),x]{\in}rad(A)$ or $[D(x),x]D^2(x){\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.
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참고문헌 (12)
참고문헌 신청
F. F. Bonsall / 1973 / Complete Normed Algebras / Berlin-Heidelberg
M. Bresar / 1988 / Jordan derivations on semiprime rings / Proc. Amer. Math. Soc. 104(4):1003~1006
M. Bresar / 1994 / Derivations of noncommutative Banach algebras II / Arch. Math. 63:56~59
M. Bresar / 2004 / Commuting maps: a survey / Taiwanese J. Math. 8(3):361~397
L. O. Chung / 1981 / Semiprime rings with nilpotent derivatives / Canad. Math. Bull. 24(4):415~421
M. Bresar / 1988 / Jordan derivations on semiprime rings / Proc. Amer. Math. Soc. 104(4):1003~1006
M. Bresar / 1994 / Derivations of noncommutative Banach algebras II / Arch. Math. 63:56~59
M. Bresar / 2004 / Commuting maps: a survey / Taiwanese J. Math. 8(3):361~397
L. O. Chung / 1981 / Semiprime rings with nilpotent derivatives / Canad. Math. Bull. 24(4):415~421
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