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Vol.21 No.4

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Derivations with Nilpotent Values on Γ-rings

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2014, v.21 no.4, pp.237-246
https://doi.org/10.7468/jksmeb.2014.21.4.237
Dey, Kalyan Kumar
Paul, Akhil Chandra
Davvaz, Bijan
Dey,, K. K. , Paul,, A. C. , & Davvaz,, B. (2014). Derivations with Nilpotent Values on Γ-rings. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 21(4), 237-246, https://doi.org/10.7468/jksmeb.2014.21.4.237

Abstract

Let M be a prime <TEX>${\Gamma}$</TEX>-ring and let d be a derivation of M. If there exists a fixed integer n such that <TEX>$(d(x){\alpha})^nd(x)=0$</TEX> for all <TEX>$x{\in}M$</TEX> and <TEX>${\alpha}{\in}{\Gamma}$</TEX>, then we prove that d(x) = 0 for all <TEX>$x{\in}M$</TEX>. This result can be extended to semiprime <TEX>${\Gamma}$</TEX>-rings.

keywords
<tex> ${\Gamma}$</tex>-ring, prime <tex> ${\Gamma}$</tex>-ring, semiprime <tex> ${\Gamma}$</tex>-ring, derivation, nilpotent <tex> ${\Gamma}$</tex>-ring

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