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ISSN : 1226-0657

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Vol.17 No.1

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LIE IDEALS AND DERIVATIONS OF σ-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
2010, v.17 no.1, pp.87-92
Shuliang, Huang
Shuliang,, H. (2010). LIE IDEALS AND DERIVATIONS OF σ-PRIME RINGS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(1), 87-92.

Abstract

Let R be a 2-torsion free <TEX>$\sigma$</TEX>-prime ring with an involution <TEX>$\sigma$</TEX>, U a nonzero square closed <TEX>$\sigma$</TEX>-Lie ideal, Z(R) the center of Rand d a derivation of R. In this paper, it is proved that d = 0 or <TEX>$U\;{\subseteq}\;Z(R)$</TEX> if one of the following conditions holds: (1) <TEX>$d(xy)\;-\;xy\;{\in}\;Z(R)$</TEX> or <TEX>$d(xy)\;-\;yx\;{\in}Z(R)$</TEX> for all x, <TEX>$y\;{\in}\;U$</TEX>. (2) <TEX>$d(x)\;{\circ}\;d(y)\;=\;0$</TEX> or <TEX>$d(x)\;{\circ}\;d(y)\;=\;x\;{\circ}\;y$</TEX> for all x, <TEX>$y\;{\in}\;U$</TEX> and d commutes with <TEX>$\sigma$</TEX>.

keywords
<tex> $\sigma$</tex>-prime ring, derivation, <tex> $\sigma$</tex>-Lie ideal

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

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