• 제목/요약/키워드: ${\ast}$-derivation

검색결과 9건 처리시간 0.022초

Generalized Derivations on ∗-prime Rings

  • Ashraf, Mohammad;Jamal, Malik Rashid
    • Kyungpook Mathematical Journal
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    • 제58권3호
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    • pp.481-488
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    • 2018
  • Let I be a ${\ast}$-ideal on a 2-torsion free ${\ast}$-prime ring and $F:R{\rightarrow}R$ a generalized derivation with an associated derivation $d:R{\rightarrow}R$. The aim of this paper is to explore the condition under which generalized derivation F becomes a left centralizer i.e., associated derivation d becomes a trivial map (i.e., zero map) on R.

APPROXIMATE LINEAR MAPPING OF DERIVATION-TYPE ON BANACH ∗-ALGEBRA

  • Chang, Ick-Soon
    • 충청수학회지
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    • 제32권2호
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    • pp.195-205
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    • 2019
  • We consider additive mappings similar to derivations on Banach ${\ast}$-algebras and we will first study the conditions for such additive mappings on Banach ${\ast}$-algebras. Then we prove some theorems concerning approximate linear mappings of derivation-type on Banach ${\ast}$-algebras. As an application, approximate linear mappings of derivation-type on $C^{\ast}$-algebra are characterized.

A FIXED POINT APPROACH TO THE STABILITY OF QUARTIC LIE ∗-DERIVATIONS

  • Kang, Dongseung;Koh, Heejeong
    • Korean Journal of Mathematics
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    • 제24권4호
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    • pp.587-600
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    • 2016
  • We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+{\frac{1}{2}}a(a^2+1)f(x-y)+(a^4-1)f(y)={\frac{1}{2}}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie ${\ast}$-derivation by using a directed method and an alternative fixed point method.

A NOTE ON NONLINEAR SKEW LIE TRIPLE DERIVATION BETWEEN PRIME ⁎-ALGEBRAS

  • Taghavi, Ali;Nouri, Mojtaba;Darvish, Vahid
    • Korean Journal of Mathematics
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    • 제26권3호
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    • pp.459-465
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    • 2018
  • Recently, Li et al proved that ${\Phi}$ which satisfies the following condition on factor von Neumann algebras $${\Phi}([[A,B]_*,C]_*)=[[{\Phi}(A),B]_*,C]_*+[[A,{\Phi}(B)]_*,C]_*+[[A,B]_*,{\Phi}(C)]_*$$ where $[A,B]_*=AB-BA^*$ for all $A,B{\in}{\mathcal{A}}$, is additive ${\ast}-derivation$. In this short note we show the additivity of ${\Phi}$ which satisfies the above condition on prime ${\ast}-algebras$.

NONLINEAR ξ-LIE-⁎-DERIVATIONS ON VON NEUMANN ALGEBRAS

  • Yang, Aili
    • Korean Journal of Mathematics
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    • 제27권4호
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    • pp.969-976
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    • 2019
  • Let ℬ(ℋ) be the algebra of all bounded linear operators on a complex Hilbert space ℋ and 𝒨 ⊆ ℬ(ℋ) be a von Neumann algebra without central abelian projections. Let ξ be a non-zero scalar. In this paper, it is proved that a mapping φ : 𝒨 → ℬ(ℋ) satisfies φ([A, B]ξ)= [φ(A), B]ξ+[A, φ(B)]ξ for all A, B ∈ 𝒨 if and only if φ is an additive ⁎-derivation and φ(ξA) = ξφ(A) for all A ∈ 𝒨.

REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS

  • Muhiuddin, G.
    • 대한수학회논문집
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    • 제31권2호
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    • pp.229-235
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    • 2016
  • In this paper we study the regularity of inside (or outside) (${\theta},{\phi}$)-derivations in BCI-algebras X and prove that let $d_{({\theta},{\phi})}:X{\rightarrow}X$ be an inside (${\theta},{\phi}$)-derivation of X. If there exists a ${\alpha}{\in}X$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a)=0$, then $d_{({\theta},{\phi})}$ is regular for all $x{\in}X$. It is also shown that if X is a BCK-algebra, then every inside (or outside) (${\theta},{\phi}$)-derivation of X is regular. Furthermore the concepts of ${\theta}$-ideal, ${\phi}$-ideal and invariant inside (or outside) (${\theta},{\phi}$)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If $d_{({\theta},{\phi})}:X{\rightarrow}X$ is an outside (${\theta},{\phi}$)-derivation of X, then $d_{({\theta},{\phi})}$ is regular if and only if every ${\theta}$-ideal of X is $d_{({\theta},{\phi})}$-invariant.

CENTRALIZING AND COMMUTING INVOLUTION IN RINGS WITH DERIVATIONS

  • Khan, Abdul Nadim
    • 대한수학회논문집
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    • 제34권4호
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    • pp.1099-1104
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    • 2019
  • In [1], Ali and Dar proved the ${\ast}$-version of classical theorem due to Posner [15, Theorem] with involution of the second kind. The main objective of this paper is to improve the above mentioned result without the condition of the second kind involution. Moreover, a related result has been discussed.

액체크로마토그래피를 이용한 수돗물 중 nitrosamine 화합물 분석의 최적화 (Optimization of analytical conditions for the determination of nitrosamines in chlorinated tap water by high performance liquid chromatography)

  • 한기찬;김희갑
    • 분석과학
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    • 제23권6호
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    • pp.551-559
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    • 2010
  • 본 연구는 칼럼 전 유도체화와 HPLC-형광검출을 이용해 염소 소독 음용수 중 7가지 nitrosamine 화합물을 분석하는 방법을 추출 과정(액-액 추출 vs. 고상 추출)과 형광 유도체화 과정(denitrosation 및 dansylation)으로 나누어 평가하여 확립하였다. 최적화된 유도체화 방법으로 두 가지의 추출법을 비교하였을 때, Ambersorb 572를 이용한 고상 추출에 대한 회수율과 재현성(상대표준편차, RSD)이 각각 54.4-88.7%와 1.9-19.4%로 액-액 추출의 51.4-87.7%와 4.2-33.3%에 비해 더 좋게 나타났다. 확립된 방법은 기존의 HPLC를 이용한 분석 방법에 비해 회수율과 재현성 모두 개선되었으며, 방법검출한계(method detection limits, MDLs)는 0.5-4.4 ng/L이었다. 이 방법으로 춘천의 염소로 소독하는 두 곳의 정수장과 10 곳의 수도꼭지에서 채취한 물 시료 중 nitrosamine 화합물을 분석한 결과, N-nitrosodimethylamine (NDMA)이 주요 화합물이었으며, 농도 범위는 26.1-112 ng/L이었다.