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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/625968 |
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