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ISSN : 1226-0657

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Vol.10 No.4
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SOME RESULTS CONCERNING (？; ')-DERIVATIONS ON PRIME 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
2003, v.10 no.4, pp.207-215
Park, Kyoo-Hong
Jung Yong-Soo
Park,, K. , & Jung, Y. (2003). SOME RESULTS CONCERNING (？; ')-DERIVATIONS ON PRIME RINGS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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, (&lt;TEX&gt;$\theta, \, \varphi$&lt;/TEX&gt;)-derivation, (&lt;TEX&gt;$\sigma, \, \tau$&lt;/TEX&gt;)-Lie ideal

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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