• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.115-142
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• 2018

This research analyzed domestic researches on early algebra education which are published in six major mathematics education journals in Korea. The purpose of this work is to grasp trends of early algebra education in Korea and to draw up future tasks. From 2000 to 2017, 89 papers which are related to early algebra education published in 6 journals. The 89 papers were categorized by research period, academic journals, research topics, and research subjects. As a result, the number of researches on early algebra education in Korea has increased since 2000. Although early algebra education belongs to the field of elementary mathematics education, lots of papers were published in other math education journals than in the math education journals for elementary school mathematics. Most research focused on proportional reasoning across the algebraic content area. The majority of the research subjects were students, especially upper-grade students of elementary school. Based on the results of this study, some implications for early algebra education in Korea were suggested.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.639-652
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• 2005

We find the class number of orders in a quaternion algebra over a dyadic local field.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.463-478
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• 2014

We find criteria for symmetrized monomials to be non-hit in the $\mathcal{A}_2$-algebra of symmetric polynomials in three variables, where $\mathcal{A}_2$ is the mod 2 Steenrod algebra.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.11-15
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• 1996

In this paper we prove that if Y is a poset of the form $\underline{1}{\oplus}Y^{\prime}$ for some subposet Y' then BCK(Y) is a ${\Gamma}$-BCK-algebra. Moreover, if X is a BCI-algebra then Hom(X, BCK(Y)) is a positive implicative ${\Gamma}$-BCK-algebra.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.29-45
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• 2004

We prove the Cauchy-Rassias stability of cyclic functional equations in Banach modules over a unital $C^*$-algebra.

• East Asian mathematical journal
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• v.4
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• pp.1-13
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• 1988

We consider some properties of the completely bounded representations of C*-algebras. We discuss the relation between the k-similarity and the property $D_k$ and get the result every k-similar C*-algebra has property $D_k$. Moreover we determine the similarity problem for the algebra C$\bigoplus$C precisely and constructively.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.583-602
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• 1995

With the theory of a certain type of orders in a Quaternion algebra, we construct Brandt matrices and theta series. As a application, we calculate the class number of a certain type of orders in a Quanternion algebra with the trace formular of Brandt matrices.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.05a
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• pp.359-360
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• 2010