A note on power values of generalized derivation in prime ring and noncommutative Banach algebras

Subject Areas : History and biography

Sh.  Sahebi ¹ (Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran)
V.  Rahmani ² (Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran)

Received: 2012-01-01 Accepted : 2012-01-01 Published : 2012-03-01

Keywords: prime ring, Banach algebras, generalized derivation, Martindale quotient ring,

Abstract :

Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivationof $R$ and $n\geq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,y\in R$; (2) obtain some related result in case $R$ is a noncommutativeBanach algebra and $H$ is continuous or spectrally bounded.

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