• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.453-459
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• 2004

A left-invariant flat Riemannian connection on a Lie group makes its Lie algebra a left symmetric algebra compatible with an inner product. The left symmetric algebra is decomposed into trivial ideal and a subalgebra of e(l). Using this result, the Lie group is embedded isomorphically into the direct product of O(l) $\times$ $R^{k}$ for some nonnegative integers l and k.

• 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. $K_s(G)$).

• The Mathematical Education
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• v.22 no.2
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• pp.5-12
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• 1984

Steenrod algebra $\alpha$$_{p}$(mod p) was generated for algebra on steenrod reduced powers p$^n$ and Bochstein coboudary operation $\beta$. We know the relation between them. In this thesis I have verified the theorem: (equation omitted)

• Honam Mathematical Journal
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• v.31 no.4
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• pp.601-609
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• 2009

The notion of generalized derivations of a BCI-algebra is introduced, and some related properties are investigated. Also, the concept of a torsion free BCI-algebra is introduced and some properties are discussed.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.611-632
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• 2009

The orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study the arithmetic properties of optimal embeddings of orders in a quaternion algebra over a dyadic local field.

• 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.

• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.10
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• pp.2064-2070
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• 2009

According to recent researches, apparent power in a non-sinusoidal single phase system can be represented with geometric algebra. In this paper, the geometric algebra is applied to apparent power defined in a multi-line system having transmission lines with frequency-dependency under non-sinusoidal conditions.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.309-313
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• 2008

The notion of central Hilbert algebras and central deductive systems is introduced, and related properties are investigated. We show that the central part of a Hilbert algebra is a deductive system. Conditions for a subset of a Hilbert algebra to be a deductive system are given. Conditions for a subalgebra of a Hilbert algebra to be a deductive system are provided.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.233-238
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• 1999

Kawamoto generalized the Witt algebra using F[${X_1}^{\pm1},....{X_n}^{\pm1}$] instead of F[x1,…, xn]. We construct the generalized Witt algebra $W_{g,h,n}$ by using additive mappings g, h from a set of integers into a field F of characteristic zero. We show that the Lie algebra $W_{g,h,n}$ is simple if a g and h are injective, and also the Lie algebra $W_{g,h,n}$ has no ad-digonalizable elements.