• 충청수학회지
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• 제22권2호
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• pp.261-269
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• 2009

We adopt the idea of $C\check{a}dariu$ and Radu to prove the stability of Jordan triple linear derivations and we take account of the Jacobson radical range problem for linear derivations.

• Kyungpook Mathematical Journal
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• 제50권3호
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• pp.379-387
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• 2010

In this paper, we present some results concerning orthogonal generalized (${\sigma},{\tau}$)-derivations in semiprime near-rings. These results are a generalization of result of Bresar and Vukman, which are related to a theorem of Posner for the product of two derivations in prime rings.

• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.355-362
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• 2010

In this note, we extend the Bresar and Vukman's result [1, Proposition 1.6], which is well-known, to higher left derivations as follows: let R be a ring. (i) Under a certain condition, the existence of a nonzero higher left derivation implies that R is commutative. (ii) if R is semiprime, every higher left derivation on R is a higher derivation which maps R into its center.

• 대한수학회논문집
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• 제34권1호
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• pp.17-26
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• 2019

In this paper, we investigate commutativity of 3-prime near-rings ${\mathcal{N}}$ in which (1, ${\alpha}$)-derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of 3-prime near-rings have been generalized. Furthermore, we give some examples show that the restriction imposed on the hypothesis is not superfluous.

• 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.

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.727-735
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• 2021

In this paper, we will study the structure of the quotient ring R/P of an arbitrary ring R by a prime ideal P. We do so using differential identities involving generalized derivations of R. We enrich our results with examples that show the necessity of their assumptions.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.95-105
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• 2023

In the present paper, we introduce a new system of functional equations, known as orthogonal Pexider hom-derivation and Pexider hom-Pexider derivation (briefly, (Pexider) hom-derivation). Using the fixed point method, we investigate the stability of Pexider hom-derivations and (Pexider) hom-derivations on Banach algebras.

• 대한수학회논문집
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• 제38권1호
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• pp.79-87
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• 2023

This paper considers some functional identities related to derivations of a ring R and their action on the centre of R/P where P is a prime ideal of R. It generalizes some previous results that are in the same spirit. Finally, examples proving that our restrictions cannot be relaxed are given.

• 대한수학회논문집
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• 제39권1호
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• pp.79-91
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• 2024

This article examines the connection between 3-derivations and the commutativity of a prime ring R with an involution * that fulfills particular algebraic identities for symmetric and skew symmetric elements. In practice, certain well-known problems, such as the Herstein problem, have been studied in the setting of three derivations in involuted rings.