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February, 2021 Generalized Derivations and Generalization of Co-commuting Maps in Prime Rings
Basudeb Dhara, Nripendu Bera, Sukhendu Kar, Brahim Fahid
Taiwanese J. Math. 25(1): 65-88 (February, 2021). DOI: 10.11650/tjm/200801


Suppose that $R$ is a prime ring of characteristic different from $2$ with Utumi quotient ring $U$, $C = Z(U)$ the extended centroid of $R$, and $f(x_1,\ldots,x_n)$ a noncentral multilinear polynomial over $C$. If $F$, $G$ and $H$ are three nonzero generalized derivations of $R$ such that \[ F\big( G(f(X)) f(X) \big) = f(X) H(f(X)) \] for all $X = (x_{1},\ldots,x_{n}) \in R^n$, then we describe the nature of the maps $F$, $G$ and $H$.


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Basudeb Dhara. Nripendu Bera. Sukhendu Kar. Brahim Fahid. "Generalized Derivations and Generalization of Co-commuting Maps in Prime Rings." Taiwanese J. Math. 25 (1) 65 - 88, February, 2021.


Received: 13 May 2020; Revised: 17 July 2020; Accepted: 2 August 2020; Published: February, 2021
First available in Project Euclid: 10 August 2020

Digital Object Identifier: 10.11650/tjm/200801

Primary: 16N60 , 16W25

Keywords: derivation‎ , extended centroid , generalized derivation , Prime ring , Utumi quotient ring

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

Vol.25 • No. 1 • February, 2021
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