• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권2호
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• pp.91-102
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• 2021

In this paper, we introduce Lie bracket Jordan derivations in Banach Jordan algebras. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of Lie bracket Jordan derivations in complex Banach Jordan algebras.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권4호
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• pp.305-313
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• 2019

Using the fixed point method, we prove the Hyers-Ulam stability of 3-Lie homomorphisms and 3-Lie derivations in 3-Lie algebras for Cauchy-Jensen functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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• pp.135-147
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• 2018

Lu et al. [27] defined derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces and proved the Hyers-Ulam stability of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces. It is easy to show that the definitions of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces are wrong and so the results of [27] are wrong. Moreover, there are a lot of seroius problems in the statements and the proofs of the results in Sections 2 and 3. In this paper, we correct the definitions of biderivations on fuzzy Banach algebras and fuzzy Lie Banach algebras and the statements of the results in [27], and prove the corrected theorems.

• 호남수학학술지
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• 제36권3호
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• pp.493-503
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• 2014

We consider the simple antisymmetrized algebra $N(e^{A_P},n,t)_1^-$. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra $N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$ of $N(e^{A_p},n,t)_k{^-}$ in this paper.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.383-387
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• 2015

In [1], the definition of C*-Lie ternary (σ,τ,ξ)-derivation is not well-defined and so the results of [1, Section 4] on C*-Lie ternary (σ,τ,ξ)-derivations should be corrected.

• 호남수학학술지
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• 제38권2호
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• pp.269-277
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• 2016

In a paper of S. H. Choi [2], the author studied the derivations of a restricted Weyl Type non-associative algebra, and determined a 1-dimensional vector space of derivations. We describe all the derivations of this algebra and prove that they form a 3-dimensional Lie algebra.

• 대한수학회논문집
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• 제32권4호
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• pp.827-833
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• 2017

In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.389-401
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• 2015

We will show the general solution of the functional equation f(x + ay) + f(x − ay) + 2(a² − 1)f(x) = a²f(x + y) + a²f(x − y) + 2a²(a² − 1)f(y) and investigate the stability of quartic Lie *-derivations associated with the given functional equation.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.887-902
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• 2023

In this article, we investigate an approximate quadratic Lie *-derivation of a quadratic functional equation f(ax + by) + abf(x - y) = (a + b)(af(x) + bf(y)), where ab ≠ 0, a, b ∈ ℕ, associated with the identity f([x, y]) = [f(x), y²] + [x², f(y)] on a 𝜌-complete convex modular *-algebra χ_𝜌 by using ∆₂-condition via convex modular 𝜌.