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http://dx.doi.org/10.7468/jksmeb.2014.21.4.237

DERIVATIONS WITH NILPOTENT VALUES ON Γ-RINGS  

Dey, Kalyan Kumar (Department of Mathematics, Rajshahi University)
Paul, Akhil Chandra (Department of Mathematics, Rajshahi University)
Davvaz, Bijan (Department of Mathematics, Yazd University)
Publication Information
The Pure and Applied Mathematics / v.21, no.4, 2014 , pp. 237-246 More about this Journal
Abstract
Let M be a prime ${\Gamma}$-ring and let d be a derivation of M. If there exists a fixed integer n such that $(d(x){\alpha})^nd(x)=0$ for all $x{\in}M$ and ${\alpha}{\in}{\Gamma}$, then we prove that d(x) = 0 for all $x{\in}M$. This result can be extended to semiprime ${\Gamma}$-rings.
Keywords
${\Gamma}$-ring; prime ${\Gamma}$-ring; semiprime ${\Gamma}$-ring; derivation; nilpotent ${\Gamma}$-ring;
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