SOME RESULTS CONCERNING (？; ')-DERIVATIONS ON PRIME RINGS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2003, v.10 no.4, pp.207-215

Park, Kyoo-Hong (Department of Mathematics Education, Seowon University)
Jung Yong-Soo (Institute of Basic Science, Seowon University)

Park, Kyoo-Hong, & Jung Yong-Soo. (2003). SOME RESULTS CONCERNING (<TEX>$\theta,\;\varphi$</TEX>)-DERIVATIONS ON PRIME RINGS. 한국수학교육학회지시리즈B:순수및응용수학, 10(4), 207-215.

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Abstract

Let R be a prime ring with characteristic different from two and let <TEX>$\theta,\varphi,\sigma,\tau$</TEX> be the automorphisms of R. Let d : <TEX>$R{\rightarrow}R$</TEX> be a nonzero (<TEX>$\theta,\varphi$</TEX>)-derivation. We prove the following results: (i) if <TEX>$a{\in}R$</TEX> and [d(R), a]<TEX>$_{{\theta}o{\sigma},{\varphi}o{\tau}}$</TEX>=0, then <TEX>$\sigma(a)\;+\;\tau(a)\;\in\;Z$</TEX>, the center of R, (ii) if <TEX>$d([R,a]_{\sigma,\;\tau)\;=\;0,\;then\;\sigma(a)\;+\;\tau(a)\;\in\;Z$</TEX>, (iii) if <TEX>$[ad(x),\;x]_{\sigma,\;\tau}\;=\;0;for\;all\;x\;\in\;RE$</TEX>, then a = 0 or R is commutative.

keywords: prime ring, (<TEX>$\theta, \, \varphi$</TEX>)-derivation, (<TEX>$\sigma, \, \tau$</TEX>)-Lie ideal

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Vol.10 No.4

SOME RESULTS CONCERNING (<TEX>$\theta,\;\varphi$</TEX>)-DERIVATIONS ON PRIME RINGS

SOME RESULTS CONCERNING (？; ')-DERIVATIONS ON PRIME RINGS

Abstract

한국수학교육학회지시리즈B:순수및응용수학