PAIR OF (GENERALIZED-)DERIVATIONS ON RINGS AND BANACH ALGEBRAS

Title & Authors
PAIR OF (GENERALIZED-)DERIVATIONS ON RINGS AND BANACH ALGEBRAS
Wei, Feng; Xiao, Zhankui;

Abstract
Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and $\small{\mu}$, $\small{\nu}$ be a pair of generalized derivations on R. If < $\small{\mu^2(x)+\nu(x),\;x^n}$ > = 0 for all x $\small{\in}$ R, then $\small{\mu}$ and $\small{\nu}$ 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 $\small{C_R}$ and d, g be a pair of derivations on R. If < $\small{d^2(x)+g(x)}$, $\small{x^n}$ > $\small{\in}$ $\small{C_R}$ for all x $\small{\in}$ 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.
Keywords
(generalized-)derivation;(semi-)prime ring;Banach algebra;
Language
English
Cited by
1.
GENERALIZED DERIVATIONS AND DERIVATIONS OF RINGS AND BANACH ALGEBRAS,;

호남수학학술지, 2013. vol.35. 4, pp.625-637
1.
GENERALIZED DERIVATIONS AND DERIVATIONS OF RINGS AND BANACH ALGEBRAS, Honam Mathematical Journal, 2013, 35, 4, 625
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