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JORDAN HIGHER DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS
Vishki, Hamid Reza Ebrahimi,Mirzavaziri, Madjid,Moafian, Fahimeh Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2
We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.
JORDAN GENERALIZED DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS
Bahmani, Mohammad Ali,Bennis, Driss,Vishki, Hamid Reza Ebrahimi,Attar, Azam Erfanian,Fahid, Barahim Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a "generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).
JORDAN 𝒢<sub>n</sub>-DERIVATIONS ON PATH ALGEBRAS
Adrabi, Abderrahim,Bennis, Driss,Fahid, Brahim Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.4
Recently, Brešar's Jordan {g, h}-derivations have been investigated on triangular algebras. As a first aim of this paper, we extend this study to an interesting general context. Namely, we introduce the notion of Jordan 𝒢<sub>n</sub>-derivations, with n ≥ 2, which is a natural generalization of Jordan {g, h}-derivations. Then, we study this notion on path algebras. We prove that, when n > 2, every Jordan 𝒢<sub>n</sub>-derivation on a path algebra is a {g, h}-derivation. However, when n = 2, we give an example showing that this implication does not hold true in general. So, we characterize when it holds. As a second aim, we give a positive answer to a variant of Lvov-Kaplansky conjecture on path algebras. Namely, we show that the set of values of a multi-linear polynomial on a path algebra KE is either {0}, KE or the space spanned by paths of a length greater than or equal to 1.
JORDAN DERIVATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS
PARK, KYOO-HONG,KIM, BYONG-DO,BYUN SANGHUN 서원대학교 기초과학연구소 2001 基礎科學硏究論叢 Vol.15 No.-
In this paper we shall give a slight generalization of J. Vukman's Theorem. And show from the result that the image of a continuous linear Jordan derivation on a noncommutative Banach algebra A is contained in the radical under the condition [D(χ), χ]E(χ) ∈ rad(A) for all χ ∈ A. And we show some properties of the derivationts on noncommutative Banach algebras. AMS Mathematics Subject Classification : 46H40.46J10,47B47 Key words and phrases : torsion free ring, derivation, Jordan derivation, prime ring, semisimple, noncommutative Banach algebra.
Lie bracket Jordan derivations in Banach Jordan algebras
Siriluk Paokanta,이정례 한국수학교육학회 2021 純粹 및 應用數學 Vol.28 No.2
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.
GENERALIZED (, )-DERIVATIONS ON POISSON BANACH ALGEBRAS AND JORDAN BANACH ALGEBRAS
Park, Chun-Gil 충청수학회 2005 충청수학회지 Vol.18 No.2
In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. In this paper, we introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalizd (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalized (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras.
Generalized $(\theta, \phi)$-Derivations on Poisson Banach Algebras and Jordan Banach Algebras
Chun-Gil Park 충청수학회 2005 충청수학회지 Vol.18 No.2
In \cite{1}, the concept of generalized $(\theta, \phi)$-derivations on rings was introduced. In this paper, we introduce the concept of generalized $(\theta, \phi)$-derivations on Poisson Banach algebras and of generalized $(\theta, \phi)$-derivations on Jordan Banach algebras, and prove the Cauchy--Rassias stability of generalized $(\theta, \phi)$-derivations on Poisson Banach algebras and of generalized $(\theta, \phi)$-derivations on Jordan Banach algebras.
JORDAN AUTOMORPHIC GENERATORS OF EUCLIDEAN JORDAN ALGEBRAS
Kim, Jung-Hwa,Lim, Yong-Do Korean Mathematical Society 2006 대한수학회지 Vol.43 No.3
In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors
선형방정식계의 해법을 중심으로 한 선형대수에서의 교수법 연구
강순부,이용균,조완영 대한수학교육학회 2010 학교수학 Vol.12 No.3
Linear algebra is not only applied compre- hensively in the branches of mathematics such as algebra, analytics, and geometry but also utilized for finding solutions in various fields such as aeronautical engineering, electronics, biology, geology, mechanics and etc. Therefore, linear algebra should be easy and comfortable for not only mathematics majors but also for general students as well. However, most find it difficult to learn linear algebra. Why is it so? It is because many studying linear algebra fail to achieve a correct understanding or attain erroneous conce- pts through misleading knowledge they already have. Such cases cause learning disability and mistakes. This research suggests more effective method of teaching by analyzing difficulty and errors made in learning system of linear equations. 선형대수는 대수학, 해석학, 기하학 등 수학의 모든 분야의 문제 해결에 광범위하게 이용될 뿐만 아니라 항공공학, 전자공학, 생물학, 지질학, 기계공학 등 다양한 학문영역에서 문제해결의 수단으로 쓰이는 이용도가 높은 학문이다. 따라서 선형대수는 수학 전공 학생뿐만 아니라 일반 학생에게도 쉽게 다가갈 수 있어야 한다. 그러나 대부분의 학생들은 선형대수 학습에서 많은 어려움을 느낀다. 왜 어려움을 느낄까? 선형대수를 학습하는 많은 학생들은 개념을 아예 인지하지 못하거나 자신들이 가지고 있던 선지식을 통해 오개념을 갖게 되고, 연이어 학습되는 부분에서 학습장애를 일으키고 오류를 범하기 때문이다. 본 연구는 선형방정식계의 학습에서 나타나는 학생들의 어려움과 오류를 분석하고 연구하여 보다 효과적인 선형대수 교수법을 제시하였다.
SINGLY GENERATED DUAL OPERATOR ALGEBRAS WITH PROPERTIES ($\mathbb{A}_{m,n}$)
Choi, Kun-Wook,Jung, Il-Bong,Lee, Sang-Hun Korean Mathematical Society 1998 대한수학회보 Vol.35 No.4
We discuss dual algebras generated by a contraction and properties $({\mathbb}A_{m,n})$ which arise in the study of the problem of solving systems of the predual of a dual algebra. In particular, we study membership for the class ${\mathbb}A_1,{{\aleph}_0 }$. As some examples we consider dual algebras generated by a Jordan block.