• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.105-108
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• 1997

In this paper we prove that if D is a continuous derivation on a noncommutative complex Banach algebra A and [D(x),x] is idempotent for every $x{\in}A$, then D maps A into its radical.

• Journal of the Korean Ceramic Society
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• v.14 no.4
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• pp.242-247
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• 1977

By means of coloring of plane nets a number of different tetrahedral frameworks can be derived. With the aid of this method all tetrahedral framework structures which built up of layer structures with 2, 4, 8 tetrahedra per unit cell and 6-membered ring or 4-8-membered ring are given. For the systematic derivation of all possible structures, graph theory may be introduced.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.387-399
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• 2008

We investigate approximately higher ternary derivations in Banach ternary algebras via the Cauchy functional equation $$f({\lambda}_{1x}+{\lambda}_{2y}+{\lambda}_{3z}={\lambda}_1f(x)+{\lambda}_2f(y)+{\lambda}_3f(z)$$.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.1-9
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• 2010

In this note, we introduce a permuting 3-derivation in nearrings and investigate the conditions for a near-ring to be a commutative ring.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.443-447
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• 2001

The main goal of this paper is to show the following: Let d and g be (continuous or discontinuous) linear derivations on a Banach algebra A over a complex field C such that $\alphad^3+dg$ is a linear Jordan derivation for some $\alpha\inC$. Then the product dg maps A into the Jacobson radical of A.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.67-79
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• 2009

We establish the generalized Hyers-Ulam-Rassias stability of higher ring derivations. Furthermore, we use the superstability of higher ring derivations to obtain approximately higher linear derivations mapping into the Jacobson radical under some conditions.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.37-48
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• 2016

The aim of this paper is to introduce the notion of a generalized derivations of BCH-algebras and some related properties are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.561-573
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• 2015

The aim of this paper is to introduce the notion of left-right (resp. right-left) symmetric bi-derivation of BCH-algebras and some related properties are investigated.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.445-454
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• 2011

In this paper, we extend some well known results concerning generalized derivations of prime rings to a generalized (${\sigma}$, ${\tau}$)-derivation.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.265-272
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• 2000

Let D be a derivation on an Banach algebra A. Suppose that [[D(x), x], D(x)] lies in the nil radical of A for all $x{\;}{\in}{\;}A$. Then D(A) is contained in the Jacobson radical of A.