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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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/
@article{KJM_2017_41_1_a6,
     author = {M. A. Raza and N. U. Rehman},
     title = {On {Generalized} {Derivation} in {Rings} and {Banach} {Algebras}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {105 },
     year = {2017},
     volume = {41},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2017_41_1_a6/}
}
TY  - JOUR
AU  - M. A. Raza
AU  - N. U. Rehman
TI  - On Generalized Derivation in Rings and Banach Algebras
JO  - Kragujevac Journal of Mathematics
PY  - 2017
SP  - 105 
VL  - 41
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KJM_2017_41_1_a6/
LA  - en
ID  - KJM_2017_41_1_a6
ER  - 
%0 Journal Article
%A M. A. Raza
%A N. U. Rehman
%T On Generalized Derivation in Rings and Banach Algebras
%J Kragujevac Journal of Mathematics
%D 2017
%P 105 
%V 41
%N 1
%U http://geodesic.mathdoc.fr/item/KJM_2017_41_1_a6/
%G en
%F KJM_2017_41_1_a6