• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.811-818
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• 2019

Let A be a Banach algebra with rad(A). We show that if there exists a continuous linear Jordan derivation D on A, then $$[D(x),x]D(x)^2{\in}rad(A)$$ if and only if $D(x)[D(x),x]D(x){\in}rad(A)$ for all $x{\in}A$.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.21-27
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• 1997

We shall define three kinds of points for algebraic varieties associated to the center 3 of U(L) which is the universal enveloping algebra of a finite-dimensional modular Lie algebra over an algebraically closed field F of prime characteristic p. We announce here that $sp_4$(F) with p = 2 has a subregular point.

• Research in Mathematical Education
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• v.9 no.2 s.22
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• pp.125-133
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• 2005

This paper investigates student conceptual understanding and application on algebra using problem-based curricula. Seven principles which National Research Council announced were considered because these seven principles all involved in the development of a deep conceptual understanding. A problem-based curriculum itself provides a significant contribution to improving student learning. A problem-based curriculum encourages students to obtain a more conceptual understanding in algebra. From the results the national curriculum developers in Korea consider the problem-based curriculum.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.271-291
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• 2021

Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The (2, 3)-cocycles of a given Hom-Lie-Yamaguti color algebra T are shown to be very useful in a study of its deformations. In particular, it is shown that any (2, 3)-cocycle of T gives rise to a Hom-Lie-Yamaguti color structure on T⊕V , where V is a T-module, and that a one-parameter infinitesimal deformation of T is equivalent to that a (2, 3)-cocycle of T (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.683-690
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• 2013

In this paper, we introduce the concept of a right derivation in incline algebras and give some properties of incline algebras. Also, the concept of d-ideal is introduced in an incline algebra with respect to right derivation.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.247-254
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• 2018

In this paper, we introduce the notion of symmetric bi-multiplier of subtraction algebra and investigate some related properties. Also, we prove that if D is a symmetric bi-multiplier of X, then D is an isotone symmetric bi-multiplier of X.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.489-499
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• 1998

Let A be the non-commutative Banach algebra with identity satisfying certain conditions. We show that if D is a derivation on A, then D(A) is contained in the radical of A.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.467-474
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• 2002

Let A be C(D), A(D), P(T), C(T), or H$\^$$\infty$/(U). We evaluate the quotient group GL(A) by exp(A).

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.97-104
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• 1997

The purpose of this paper is to prove the following result: Let A be a noncommutative semisimple Banach algebra. Suppose that $D:A{\rightarrow}A$, $G:A{\rightarrow}A$ are linear derivations such that [G(x), x]D(x) = D(x)[G(x), x] = 0, [D(x), G(x)] = 0 hold for all $x{\in}A$. In this case either D = 0 or G = 0.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.671-678
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• 2005

Let R be a noncommutative semi prime ring. Suppose that there exists a derivation d : R $\to$ R such that for all x $\in$ R, either [[d(x),x], d(x)] = 0 or $\langle$$\langle(x),\;x\rangle,\;d(x)\rangle$ = 0. In this case [d(x), x] is nilpotent for all x $\in$ R. We also apply the above results to a Banach algebra theory.