Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PAIR OF (GENERALIZED-)DERIVATIONS ON RINGS AND BANACH ALGEBRAS

  • Wei, Feng (DEPARTMENT OF MATHEMATICS BEIJING INSTITUTE OF TECHNOLOGY) ;
  • Xiao, Zhankui (DEPARTMENT OF MATHEMATICS BEIJING INSTITUTE OF TECHNOLOGY)
  • Published : 2009.09.30
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Abstract

Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and $\mu$, $\nu$ be a pair of generalized derivations on R. If < $\mu^2(x)+\nu(x),\;x^n$ > = 0 for all x $\in$ R, then $\mu$ and $\nu$ are either left multipliers or right multipliers. Let n be a fixed positive integer, R be a noncommutative 2n!-torsion free prime ring with the center $C_R$ and d, g be a pair of derivations on R. If < $d^2(x)+g(x)$, $x^n$ > $\in$ $C_R$ for all x $\in$ R, then d = g = 0. Then we apply these purely algebraic techniques to obtain several range inclusion results of pair of (generalized-)derivations on a Banach algebra.

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