• Kyungpook Mathematical Journal
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• 제23권2호
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• pp.169-173
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• 1983

• 대한수학회지
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• 제12권1호
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• pp.29-35
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• 1975

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.263-271
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• 1997

In this paper we show that every left derivation on a semiprime Banach algebra A is a derivation which maps A into the intersection of the center of A and the jacobson radical of A and hence every left derivation on a semisimple Banach algebra is always zero.

• 충청수학회지
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• 제24권3호
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• pp.543-551
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• 2011

In this paper, we consider the functional inequalities with approximately centralizing derivations on noncommutative Banach algebras, and investigate the problem that functions satisfying the functional inequalities mentioned above map into the radical.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.737-750
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• 2016

In this note we describe some classes of rings in relation to Abelian property of factorizations by nilradicals and Jacobson radical. The ring theoretical structures are investigated for various sorts of such factor rings which occur in the process.

• 대한수학회논문집
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• 제33권1호
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• pp.103-125
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• 2018

Let R be a 5!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. Then $[D(x),x]D(x)^2=0$ if and only if $D(x)^2[D(x), x]=0$ for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A) and if D is a continuous linear Jordan derivation on A, then we show that $[D(x),x]D(x)2{\in}rad(A)$ if and only if $D(x)^2[D(x),x]{\in}rad(A)$ for all $x{\in}A$ where rad(A) is the Jacobson radical of A.

• 대한수학회논문집
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• 제34권1호
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• pp.43-54
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• 2019

Let R be a ring with identity and J(R) denote the Jacobson radical of R, i.e., the intersection of all maximal left ideals of R. A ring R is called J-symmetric if for any $a,b,c{\in}R$, abc = 0 implies $bac{\in}J(R)$. We prove that some results of symmetric rings can be extended to the J-symmetric rings for this general setting. We give many characterizations of such rings. We show that the class of J-symmetric rings lies strictly between the class of symmetric rings and the class of directly finite rings.

• 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.

• 대한수학회보
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• 제38권4호
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• pp.709-718
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• 2001

In this paper we show that if D and G are continuous linear Jordan derivations on a Banach algebra A satisfying [D(x), x]x - x[G(x),x] $\epsilon$ rad(A)for all $\epsilon$ A, then both D and G map A into rad(A).

• 충청수학회지
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• 제8권1호
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• pp.37-44
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• 1995

In this paper we show that every left derivation on a semiprime Banach algebra A is a derivation which maps A into the intersection of the center of A and the Jacobson radical of A, and hence every left derivation on a semisimple Banach algebra is zero.