• 대한수학회논문집
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• 제28권3호
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• pp.535-558
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• 2013

The purpose of this paper is to prove that the noncommutative version of the Singer-Wermer Conjecture is affirmative under certain conditions. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $D(x)^3[D(x),x]{\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.119-125
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• 2007

In this paper, we investigate the following: Let A be a semisimple Banach algebra. Suppose that there exists a linear derivation $f:A{\rightarrow}A$ such that the functional equation $<f(x),x>^2=0$ holds for all $x{\in}A$. Then we have $f=0$ on A.

• 충청수학회지
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• 제29권3호
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• pp.443-451
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• 2016

In this paper, we introduce the concept of a symmetric bi-f-multiplier in incline algebras and give some properties of incline algebras. Also, we characterize Ker(D) and $Fix_a(D)$ by symmetric bi-f-multipliers in incline algebras.

• 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.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.497-505
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• 2013

The noncommutative Singer-Wermer conjecture states that every derivation on a Banach algebra (possibly noncommutative) leaves primitive ideals of the algebra invariant. This conjecture is still an open question for more than thirty years. In this note, we approach this question via some sufficient conditions for the separating ideal of ${\phi}$-derivations to be nilpotent. Moreover, we show that the spectral boundedness of ${\phi}$-derivations implies that they leave each primitive ideal of Banach algebras invariant.

• Bulletin of the Korean Chemical Society
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• 제30권2호
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• pp.315-318
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• 2009

Some particular bound state energies of an electron, under Coulomb potential field, confined in a two-dimensional circle and a three-dimensional sphere are analytically derived. The derivation shows that the electron cannot be bound in a negative energy state when the circle (or sphere) is smaller than a certain critical size. The critical size dependency on the strength of Coulomb potential and the angular momentum of the electron is also analytically derived. This system mimics quantum dots. Therefore the derivation provides new information on a minimum critical size of quantum dots with hydrogenic impurity.

• 호남수학학술지
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• 제40권2호
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• pp.227-237
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• 2018

There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra. We find all the derivations of a growing algebra in the paper. The dimension of derivations of the growing algebra is one and every derivation of the growing algebra is outer. We show that there is a class of purely outer algebras in this work.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.381-387
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• 2002

Our main goal is to show that if there Jordan derivation D, G on a noncommutative (n+1)!-torsion free prime ring R such that D($\chi$)$\chi$$^n$+$\chi$$^n$G($\chi$) $\in$ C(R) for all $\chi$ $\in$ R, then we have D=0 and G=0.

• 한국결정학회지
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• 제9권1호
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• pp.39-43
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• 1998

결정면 법선의 각좌표와 Laue 회절 반점의 각좌표 사이의 관계를 나타내는 기존의 기하도형을 개선하였다. 그래서 Greninger와 Leonhardt charts에서의 선들에 대한 Bernalte의 대수방정식을 보다 더 직관적으로 그리고 보다 더 명료하게 도출하였다.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.343-347
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• 2016

Posner's first theorem states that if R is a prime ring of characteristic different from two, $d_1$ and $d_2$ are derivations on R such that the iterate $d_1d_2$ is also a derivation of R, then at least one of $d_1$, $d_2$ is zero. In the present paper we extend this result to *-prime rings of characteristic different from two.