• Journal of the Korean School Mathematics Society
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• v.12 no.1
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• pp.99-114
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• 2009

Although they are interested in Linear Algebra not only in science and engineering but also in humanities and sociology recently, a study of teaching linear algebra is not relatively abundant because linear algebra was taken as basic course in colleges just for 20-30 years. However, after establishing The Linear Algebra Curriculum Study Group in January, 1990, a variety of attempts to improve teaching linear algebra have been emerging. This article looks into series of studies related with teaching matrix. For this the method for teaching the concepts of matrix in relation to historico-genetic principle looking through the process of the conceptual development of matrix-determinants, matrix-systems of linear equations and linear transformation.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.583-593
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• 2005

The Weyl-type non-associative algebra ${\overline{WN_{g_n,m,s_r}}$ and its subalgebra ${\overline{WN_{n,m,s_r}}$ are defined and studied in the papers [2], [3], [9], [11], [12]. We find the derivation group $Der_{non}({\overline{WN_{1,0,0_{[2]}}})$ the non-associative simple algebra ${\overline{WN_{1,0,0_{[2]}}}$.

• Honam Mathematical Journal
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• v.7 no.1
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• pp.119-127
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• 1985

A study is made of a special type of $C^{\ast}$ -dynamical systems, consisting of a class $n^{\infty}$ uniformly hyperfinite $C^{\ast}$-algebra A, the torus group $G=T^{d}$ ($$1{\leq_-}d{\leq_-}n-1$$) and a natural product action of G on A by $^{*}-automorphisms$. We give some conditions for product states on the fixed point algebra $A^{G}$ of A by G to be factorial.

• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.1-8
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• 1999

Let $K_{\alpha}(G)$ (resp. $K_s(G)$) be the abelian (resp. symmetric) Kac algebra for a locally compact group G. We show that there exists a one-to-one correspondence between the subgroups of G and the sub-Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$). Moreover we obtain similar correspondences between the subgroups of G and the reduced Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$).

• East Asian mathematical journal
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• v.15 no.2
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• pp.313-324
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• 1999

What we will be concerned with is, first, the question of the condition about $\mathcal{L}$ that gives Alg$\mathcal{L}$ a von Neumann algebra, that is, the question of the condition about $\mathcal{L}$ that will give Alg$\mathcal{L}$ a self-adjoint algebra. Secondly, if Alg$\mathcal{L}$ is a von Neumann algebra, we want to find out what type it is.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.749-755
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• 2010

We investigate biprojectivity of $C_{r}^{*}(G)$ as a $L^1(G)$-bimodule for a locally compact group G. The main results are the following. As a $L^1(G)$-bimodule$C_{r}^{*}(G)$ is biprojective if G is compact and is not biprojective if G is an infinite discrete group or G is a non-compact abelian group.

• East Asian mathematical journal
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• v.21 no.2
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• pp.151-161
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• 2005

We analyze the structure of $C^*-algebras$ generated by left regular isometric representations of semigroups.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.159-175
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• 2006

This paper is a survey on the Hyers-Ulam-Rassias stability of the Jensen functional equation in $C^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Its content is divided into the following sections: 1. Introduction and preliminaries. 2. Approximate isomorphisms in $C^*$-algebras. 3. Approximate isomorphisms in Lie $C^*$-algebras. 4. Approximate isomorphisms in $JC^*$-algebras. 5. Stability of derivations on a $C^*$-algebra. 6. Stability of derivations on a Lie $C^*$-algebra. 7. Stability of derivations on a $JC^*$-algebra.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.669-682
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• 2016

In this paper, we study the cellular structure of the G-edge colored partition algebras, when G is a finite group. Further, we classified all the irreducible representations of these algebras using their cellular structure whenever G is a finite cyclic group. Also we prove that the ${\mathbb{Z}}/r{\mathbb{Z}}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.29-36
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• 1998

We show that if M is a $II_1$-factor and a countable discrete group G acts outerly on M then Jones' index $[M:M^G]$ of a pair of $II_1^-factors is equal to the order $\mid$G$\mid$ of G. It is also shown that for a subgroup H of G Jones' index $[M^H:M^G]$ is equal to the group index [G:H] under certain conditions.