Geodesic
On Generalized Derivation in Rings and Banach Algebras
Kragujevac Journal of Mathematics, Tome 41 (2017) no. 1, p. 105 .

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Let $R$ be a prime ring, $F$ be a generalized derivation associated with a derivation $d$ of $R$ and $m,n$ be the fixed positive integers. In this paper we study the case when one of the following holds: (i) $F(x)\circ_m F(y)=(x\circ y)^n$, (ii) $F(x)\circ_m d(y)=d(x\circ y)^n$ for all $x,y$ in some appropriate subset of $R$. We also examine the case where $R$ is a semiprime ring. Finally, as an application we obtain some range inclusion results of continuous or spectrally bounded generalized derivations on non-commutative Banach algebras.
Classification : 16W25 16N60, 16U80
Keywords: Prime and semiprime rings, generalized derivation, generalized polynomial identity (GPI), ideal 
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     author = {M. A. Raza and N. U. Rehman},
     title = {On {Generalized} {Derivation} in {Rings} and {Banach} {Algebras}},
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     pages = {105 },
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     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2017_41_1_a6/}
}
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M. A. Raza; N. U. Rehman. On Generalized Derivation in Rings and Banach Algebras. Kragujevac Journal of Mathematics, Tome 41 (2017) no. 1, p. 105 . http://geodesic.mathdoc.fr/item/KJM_2017_41_1_a6/