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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.10 No.4

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

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

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 10(4), 207-215.

Abstract

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

한국수학교육학회지시리즈B:순수및응용수학

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