• 제목/요약/키워드: Lie ideals

검색결과 27건 처리시간 0.026초

EXTENSION OF FUZZY LIE SUBALGEBRAS AND FUZZY LIE IDEALS ON U(L)

  • Kim, Chung-Gook;Kim, Hee-Sik
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 1996년도 추계학술대회 학술발표 논문집
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    • pp.101-103
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    • 1996
  • In this note we will discuss extension of fuzzy Lie subalgebra and fuzzy Lie ideals of a Lie algebra L on universal enveloping algebra U(L) of L and will study some relations among them.

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LIE IDEALS IN TRIDIAGONAL ALGEBRA ALG𝓛

  • Kang, Joo Ho
    • 대한수학회보
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    • 제52권2호
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    • pp.351-361
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    • 2015
  • We give examples of Lie ideals in a tridiagonal algebra $Alg\mathcal{L}_{\infty}$ and study some properties of Lie ideals in $Alg\mathcal{L}_{\infty}$. We also investigate relationships between Lie ideals in $Alg\mathcal{L}_{\infty}$. Let k be a fixed natural number. Let $\mathcal{A}$ be a linear manifold in $Alg\mathcal{L}_{\infty}$ such that $T_{(2k-1,2k)}=0$ for all $T{\in}\mathcal{A}$. Then $\mathcal{A}$ is a Lie ideal if and only if $T_{(2k-1,2k-1)}=T_{(2k,2k)}$ for all $T{\in}\mathcal{A}$.

ON FUZZY IDBALS OF LIE ALGEBRAS

  • Jun, Young-Bae;Kim, Kyung-Ho;Roh, Eun-Hwan
    • Journal of applied mathematics & informatics
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    • 제10권1_2호
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    • pp.251-259
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    • 2002
  • The fuzzification of an ideal in a Lie algebra is considered. Using a level subset of a fuzzy subset of a Lie algebra, we give a characterization of a fuzzy ideal, and using a family of ideals of a Lie algebra, we establish a fuzzy ideal. With relation to the ascending chain of ideals, a characterization for the set of values of any fuzzy ideal to be a well-ordered subset of the closed unit interval [0,1] is stated.

ON GENERALIZED LIE IDEALS IN SEMI-PRIME RINGS WITH DERIVATION

  • Ozturk, M. Ali;Ceven, Yilmaz
    • East Asian mathematical journal
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    • 제21권1호
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    • pp.1-7
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    • 2005
  • The object of this paper is to study($\sigma,\;\tau$)-Lie ideals in semi-prime rings with derivation. Main result is the following theorem: Let R be a semi-prime ring with 2-torsion free, $\sigma$ and $\tau$ two automorphisms of R such that $\sigma\tau=\tau\sigma$=, U be both a non-zero ($\sigma,\;\tau$)-Lie ideal and subring of R. If $d^2(U)=0$, then d(U)=0 where d a non-zero derivation of R such that $d\sigma={\sigma}d,\;d\tau={\tau}d$.

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COMMUTATORS AND ANTI-COMMUTATORS HAVING AUTOMORPHISMS ON LIE IDEALS IN PRIME RINGS

  • Raza, Mohd Arif;Alhazmi, Hussain
    • Korean Journal of Mathematics
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    • 제28권3호
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    • pp.603-611
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    • 2020
  • In this manuscript, we discuss the relationship between prime rings and automorphisms satisfying differential identities involving commutators and anti-commutators on Lie ideals. In addition, we provide an example which shows that we cannot expect the same conclusion in case of semiprime rings.

FUZZY LIE IDEALS AND FUZZY LIE SUBALGEBRAS

  • Kim, Chung-Gook
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 1995년도 추계학술대회 학술발표 논문집
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    • pp.339-346
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    • 1995
  • In this paper we tried to apply the concepts of fuzzy set to Lie algebra, to define some concepts related to fuzzy set to discuss their properties and relations among them.

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NOTES ON (σ, τ)-DERIVATIONS OF LIE IDEALS IN PRIME RINGS

  • Golbasi, Oznur;Oguz, Seda
    • 대한수학회논문집
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    • 제27권3호
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    • pp.441-448
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    • 2012
  • Let R be a prime ring with center Z and characteristic different from two, U a nonzero Lie ideal of R such that $u^2{\in}U$ for all $u{\in}U$ and $d$ be a nonzero (${\sigma}$, ${\tau}$)-derivation of R. We prove the following results: (i) If $[d(u),u]_{{\sigma},{\tau}}$ = 0 or $[d(u),u]_{{\sigma},{\tau}}{\in}C_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$. (ii) If $a{\in}R$ and $[d(u),a]_{{\sigma},{\tau}}$ = 0 for all $u{\in}U$, then $U{\subseteq}Z$ or $a{\in}Z$. (iii) If $d([u,v])={\pm}[u,v]_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$.