• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.297-304
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• 2012

There are several types of orders in a Quaternion algebra. Generally, zeta functions defined on orders of a Quaternion algebra give some informations on the ideal theory of orders. In this study, we investigate functional equalities between the zeta functions defined on orders of a Quaternion algebra.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1333-1354
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• 2019

In authors' paper in 2007, it was shown that the BSE-extension of $C^1_0(R)$, the algebra of continuously differentiable functions f on the real number space R such that f and df /dx vanish at infinity, is the Lipschitz algebra $Lip_1(R)$. This paper extends this result to the case of $C^n_0(R^d)$ and $C^{n-1,1}_b(R^d)$, where n and d represent arbitrary natural numbers. Here $C^n_0(R^d)$ is the space of all n-times continuously differentiable functions f on $R^d$ whose k-times derivatives are vanishing at infinity for k = 0, ${\cdots}$, n, and $C^{n-1,1}_b(R^d)$ is the space of all (n - 1)-times continuously differentiable functions on $R^d$ whose k-times derivatives are bounded for k = 0, ${\cdots}$, n - 1, and (n - 1)-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(R^d)$ has a predual.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.739-746
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• 2013

There are several ways to normalize a Haar measure on the orders in a quaternion algebra. In order to understand the arithmetic properties of orders, we study the volumes of orders and compute them for some cases.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.73-82
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• 2013

There are some identities between the representations of Hecke operators defined on a subspace of modular forms associated with orders of a Quaternion algebra. In this paper, we find the identities between the zeta functions attached to these representations.

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.71-78
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• 2000

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.789-830
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• 2003

By forming completions of families of noncommutative polynomials, we define a notion of noncommutative continuous function and locally bounded Borel function that give a noncommutative analogue of the functional calculus for elements of commutative $C^{*}$-algebras and von Neumann algebras. These notions give a precise meaning to $C^{*}$-algebras defined by generator and relations and we show how they relate to many parts of operator and operator algebra theory.

• School Mathematics
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• v.2 no.1
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• pp.183-202
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• 2000

The purpose of this study is to restructure the 10th grade mathematics curriculum for teaching the function area under the computer environment using ‘Mathview’, which is a computer algebra system designed for exploring algebra dynamically. The instructional sequence of the function area was redesigned to highlight the functions and properties of the computer software. And, based on the newly designed sequence, this study develops the sample ‘teaching unit’ using Mathview. The basic principle of the materials is to encourage students to investigate mathematics by manipulate various experimental tasks by themselves or through group study. And, the draft of the sequence and teaching unit was reviewed by some mathematics teachers and revised through the feedback.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.585-602
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• 2019

We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.119-129
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• 2021

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