On Prime-Gamma-Near-Rings with Generalized Derivations

Let 𝑁 be a 2-torsion free prime Γ-near-ring with center 𝑍(𝑁). Let (𝑓,𝑑) and (𝑔,ℎ) be two generalized derivations on 𝑁. We prove the following results: (i) if 𝑓([𝑥,𝑦]𝛼)=0 or 𝑓([𝑥,𝑦]𝛼)=±[𝑥,𝑦]𝛼 or 𝑓2(𝑥)∈𝑍(𝑁) for all 𝑥,𝑦∈𝑁, 𝛼∈Γ, then 𝑁 is a commutative Γ-ring. (ii) If 𝑎∈𝑁 and [𝑓(𝑥),𝑎]𝛼=0 for all 𝑥∈𝑁, 𝛼∈...

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Bibliographic Details
Main Authors: Kalyan Kumar Dey, Akhil Chandra Paul, Isamiddin S. Rakhimov
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/625968
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