• 대한수학회보
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• 제47권6호
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• pp.1121-1129
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• 2010

In the present paper, we extend some well known results concerning derivations of prime rings to generalized derivations for ($\sigma,\tau$)-Lie ideals.

• 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.

• 호남수학학술지
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• 제29권2호
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• pp.259-268
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• 2007

The notion of intuitionistic fuzzy Lie ideal of a Lie algebra is introduced, and related properties are investigated. Characterizations of an intuitionistic fuzzy Lie ideal are provided. Using a collection of Lie ideals, an intuitionistic fuzzy Lie ideal is established.

• 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 $T{\in}\mathcal{A}$.

• 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.

• 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 $d\sigma={\sigma}d,\;d\tau={\tau}d$.

• 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.

• East Asian mathematical journal
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• 제36권1호
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• pp.101-114
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• 2020

In this paper, we investigate commutativity of semiprime rings with a derivation which is strongly commutativity preserving and acts as a homomorphism or as an anti-homomorphism on a nonzero Lie ideal.

• 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.

• 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 $U{\subseteq}Z$.