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

ISSN : 3059-0604

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Vol.17 No.1

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LIE IDEALS AND DERIVATIONS OF $\sigma$-PRIME RINGS

LIE IDEALS AND DERIVATIONS OF σ-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
2010, v.17 no.1, pp.87-92
Shuliang, Huang (DEPARTMENT OF MATHEMATICS, CHUZHOU UNIVERSITY)
Shuliang, Huang. (2010). LIE IDEALS AND DERIVATIONS OF <TEX>$\sigma$</TEX>-PRIME RINGS, 17(1), 87-92.

Abstract

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

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

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한국수학교육학회지시리즈B:순수및응용수학

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