• 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.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.211-217
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• 2011

In this paper we study some properties on regular homomorphisms. In particular, we investigate the equivalent conditions for the homomorphism of minimal sets to be regular.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.183-197
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• 2012

Geometry having long history of mathematics have important role for thinking power and creativity progress in middle school. The regular polygon included in plane geometry was mainly taught convex regular polygon in elementary school and middle school. In this study, we investigated the denotation's extension of regular polygon by mathematical basic knowledge included in school curriculum. For this research, first, school mathematical knowledge about regular polygon was analyzed. And then, basic direction of research was established for inquiry. Second, based on this analysis inductive inquiry activity was performed with research using geometry software(Cabri Geometry II). Through this study the development of enriched learning material and showing the direction of geometry research is expected.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.525-527
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• 2019

Let X be a completely regular space and let β(X) be the Stone-Čech compactification of X. A flow 𝜙 on X can be extended to a flow 𝚽 on β(X).

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.119-130
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• 1995

I study the extension of the definition of the analytic operator-valued Feynman integral to potentials given by a class of signed measures described in terms of additive functionals associated with regular Dirichlet forms.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.235-243
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• 2009

In this paper, we introduce the notion of intuitionistic fuzzy semiprimality in an ordered semigroup, which is an extension of fuzzy semiprimality and investigate some properties of intuitionistic fuzzification of the concept of several ideals.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.363-372
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• 2024

In this paper, we introduce a weak version of coherent that we call regular coherent property. A ring is called regular coherent, if every finitely generated regular ideal is finitely presented. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.93-103
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• 2020

This article concerns a property of Abelain π-regular rings. A ring R shall be called right quasi-DR if for every a ∈ R there exists n ≥ 1 such that C(R)aⁿ ⊆ aR, where C(R) means the monoid of regular elements in R. The relations between the right quasi-DR property and near ring theoretic properties are investigated. We next show that the class of right quasi-DR rings is quite large.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.991-1018
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• 2006

Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product $\Delta=C_2*C_2*C_2$. In this correspondence, hypermaps correspond to conjugacy classes of subgroups of $\Delta$, and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out$(\Delta)$ of the triangle group $\Delta$. This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups $\Theta$ of $\Delta$ of finite index. This generalises the notion of regularity to some non-regular objects.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.837-851
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• 2021

Let R ⊆ L ⊆ S be ring extensions. Two star operations ${\ast}_1{\in}Star(R,S)$, ${\ast}_2{\in}Star(L,S)$ are said to be linked if whenever $A^{{\ast}_1}= R^{{\ast}_1}$ for some finitely generated S-regular R-submodule A of S, then $(AL)^{{\ast}_2}=L^{{\ast}_2}$. We study properties of linked star operations; especially when ${\ast}_1$ and ${\ast}_2$ are strict star operations. We introduce the notion of Prüfer star multiplication extension ($P{\ast}ME$) and we show that under appropriate conditions, if the extension R ⊆ S is $P{\ast}_1ME$ and ${\ast}_1$ is linked to ${\ast}_2$, then L ⊆ S is $P{\ast}_2ME$.