• 제목/요약/키워드: ${\sigma}$-derivation

검색결과 46건 처리시간 0.035초

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

  • Park, Kyoo-Hong;Jung Yong-Soo
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제10권4호
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    • pp.207-215
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    • 2003
  • 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.

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SOME RESULTS ON GENERALIZED LIE IDEALS WITH DERIVATION

  • Aydin, Neset;Kaya, Kazim;Golbasi, Oznur
    • East Asian mathematical journal
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    • 제17권2호
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    • pp.225-232
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    • 2001
  • Let R be a prime ring with characteristic not two. U a (${\sigma},{\tau}$)-left Lie ideal of R and d : R$\rightarrow$R a non-zero derivation. The purpose of this paper is to invesitigate identities satisfied on prime rings. We prove the following results: (1) [d(R),a]=0$\Leftrightarrow$d([R,a])=0. (2) if $(R,a)_{{\sigma},{\tau}}$=0 then $a{\in}Z$. (3) if $(R,a)_{{\sigma},{\tau}}{\subset}C_{{\sigma},{\tau}}$ then $a{\in}Z$. (4) if $(U,a){\subset}Z$ then $a^2{\in}Z\;or\;{\sigma}(u)+{\tau}(u){\in}Z$, for all $u{\in}U$. (5) if $(U,R)_{{\sigma},{\tau}}{\subset}C_{{\sigma},{\tau}}$ then $U{\subset}Z$.

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

  • Shuliang, Huang
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제17권1호
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    • pp.87-92
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    • 2010
  • 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 $\sigma$.

식스시그마와 PM의 비교 (Comparision of Six Sigma and PM)

  • 최성운
    • 대한안전경영과학회:학술대회논문집
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    • 대한안전경영과학회 2005년도 춘계학술대회
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    • pp.109-116
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    • 2005
  • This paper discusses the relationship between project management and six sigma and the derivation of overall related table. This paper proposes an integrated approach by blending CMM project management and six sigma to meet business goals.

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INNER DERIVATIONS MAPPING INTO THE RADICAL

  • Jun, Kil-Woung;Lee, Young-Whan
    • Journal of applied mathematics & informatics
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    • 제5권3호
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    • pp.889-893
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    • 1998
  • In this paper we show that $\sigma$a maps into the radical if and only if for every irreducible representation $\pi$,$\pi$(a) is scalar and obtain that every inner derivation corresponding to $\sigma$-quasi central elements in some Banach algebra maps into the radical.

On The Derivation of a Certain Noncentral t Distribution

  • Gupta, A.K.;Kabe, D.G.
    • Journal of the Korean Statistical Society
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    • 제19권2호
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    • pp.182-185
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    • 1990
  • Let a p-component vector y have a p-variate normal distribution $N(b\theta, \Sigma), \Sigma$ unknown, b specified, then for testing $\theta = 0$ against general $\theta$, Khatri and Rao (1987) derive a certain t test and obtain its power function. This paper presents a direct derivation of this power function in terms of the original variates unlike Khatri and Rao (1987) who resort to the canonical transformations of the original variates and the conditional distributions.

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PRIME RADICALS IN ORE EXTENSIONS

  • Han, Jun-Cheol
    • East Asian mathematical journal
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    • 제18권2호
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    • pp.271-282
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    • 2002
  • Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

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On Commutativity of σ-Prime Γ-Rings

  • DEY, KALYAN KUMAR;PAUL, AKHIL CHANDRA;DAVVAZ, BIJAN
    • Kyungpook Mathematical Journal
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    • 제55권4호
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    • pp.827-835
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    • 2015
  • Let U be a ${\sigma}$-square closed Lie ideal of a 2-torsion free ${\sigma}$-prime ${\Gamma}$-ring M. Let $d{\neq}1$ be an automorphism of M such that $[u,d(u)]_{\alpha}{\in}Z(M)$ on U, $d{\sigma}={\sigma}d$ on U, and there exists $u_0$ in $Sa_{\sigma}(M)$ with $M{\Gamma}u_0{\subseteq}U$. Then, $U{\subseteq}Z(M)$. By applying this result, we generalize the results of Oukhtite and Salhi respect to ${\Gamma}$-rings. Finally, for a non-zero derivation of a 2-torsion free ${\sigma}$-prime $\Gamma$-ring, we obtain suitable conditions under which the $\Gamma$-ring must be commutative.