• 대한수학회지
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• 제34권4호
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• pp.1009-1018
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• 1997

Observing that for any $\beta_c$-Wallman functor $A$ and any Tychonoff space X, there is a cover $(C_1(A(X), X), c_1)$ of X such that X is $A$-disconnected if and only if $c_1 : C_1(A(X), X) \longrightarrow X$ is a homeomorphism, we show that every Tychonoff space has the minimal $A$-disconnected cover. We also show that if X is weakly Lindelof or locally compact zero-dimensional space, then the minimal G-disconnected (equivalently, cloz)-cover is given by the space $C_1(A(X), X)$ which is a dense subspace of $E_cc(\betaX)$.

• 한국수학사학회지
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• 제18권4호
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• pp.113-124
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• 2005

티코노프공간 X에 대하여 C(X)와 $C^*(X)$는 Riesz-공간이다 C(X)가 순서-코시완비일 필요충분한조건은 X가 quasi-F 공간이고, X가 컴팩트공간이며 QF(X)가 X의 극소 quasi-F cover일 때, C(X)의 순서-코시완비화와 C(QF(X))는 동형이다. 본 논문에서는 quasi-F 공간의 정의와 극소 quasi-F cover의 구성에 관한 동기 및 역사적 배경을 살펴본다.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.185-190
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• 2022

The aim of this article is to define fuzzy maximal open cover and discuss its few properties. we also defined and study fuzzy m-compact space and discussed its properties. Also we obtain few more results on fuzzy minimal c-regular and fuzzy minimal c-normal spaces. We have proved that a fuzzy Haussdorff m-compact space is fuzzy minimal c-normal.

• 대한수학회논문집
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• 제21권2호
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• pp.347-353
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• 2006

In this paper, we show that if the minimal basically disconnected cover ${\wedge}X_\imath\;of\;X_\imath$ is given by the space of fixed a $Z(X)^#$-ultrafilters on $X_\imath\;(\imath=1,2)\;and\;{\wedge}X_1\;{\times}\;{\wedge}X_2$ is a basically disconnected space, then ${\wedge}X_1\;{\times}\;{\wedge}X_2$ is the minimal basically disconnected cover of $X_1\;{\times}\;X_2$. Moreover, observing that the product space of a P-space and a countably locally weakly Lindelof basically disconnected space is basically disconnected, we show that if X is a weakly Lindelof almost P-space and Y is a countably locally weakly Lindelof space, then (${\wedge}X\;{\times}\;{\wedge}Y,\;{\wedge}_X\;{\times}\;{\wedge}_Y$) is the minimal basically disconnected cover of $X\;{\times}\;Y$.

• 대한수학회보
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• 제52권3호
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• pp.977-986
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• 2015

Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.

• 대한수학회지
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• 제39권4호
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• pp.611-620
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• 2002

The aim of the Paper is to Obtain information about the flat covers and minimal flat resolutions of Artinian modules over a Noetherian ring. Let R be a commutative Noetherian ring and let A be an Artinian R-module. We prove that the flat cover of a is of the form $\prod_{p\epsilonAtt_R(A)}T-p$, where $Tp$ is the completion of a free R$_{p}$-module. Also, we construct a minimal flat resolution for R/xR-module 0: $_AX$ from a given minimal flat resolution of A, when n is a non-unit and non-zero divisor of R such that A = $\chiA$. This result leads to a description of the structure of a minimal flat resolution for ${H^n}_{\underline{m}}(R)$, nth local cohomology module of R with respect to the ideal $\underline{m}$, over a local Cohen-Macaulay ring (R, $\underline{m}$) of dimension n.

• 한국토양비료학회지
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• 제48권1호
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• pp.15-21
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• 2015

The use of cover crops has a beneficial effect on sustainable soil management in pear orchards. We aimed to compare changes in soil chemical properties and biota with the use of different cover crops. We tested the effects of five cover plants, including hairy vetch, orchard grass, rattail fescue, rye, and perennial ryegrass. Use of different cover crops had a minimal impact on soil chemical properties through three year experiments. The aboveground biomass was greatest with the use of rye. The potential amounts of returnable N and P were highest when leguminous hairy vetch was used as a cover plant. Changes in the composition of the microbial community were investigated by phospholipid fatty acid (PLFA) analysis. Microbial PLFAs were highest with the use of rattail fescue and lowest with the use of hairy vetch. Minimal changes in the abundances of nematodes and microarthropods suggested that there was no bottom-up control in the soil ecosystem. The results also show that increases in aboveground biomass and nutrient content with the use of cover crops may not promote the abundance of soil organisms.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.517-524
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• 2012

In this paper, we first show that for any space X, there is a Boolean subalgebra $\mathcal{G}(z_X)$ of R(X) containg $\mathcal{G}(X)$. Let X be a strongly zero-dimensional space such that $z_{\beta}^{-1}(X)$ is the minimal cloz-coevr of X, where ($E_{cc}({\beta}X)$, $z_{\beta}$) is the minimal cloz-cover of ${\beta}X$. We show that the minimal cloz-cover $E_{cc}(X)$ of X is a subspace of the Stone space $S(\mathcal{G}(z_X))$ of $\mathcal{G}(z_X)$ and that $E_{cc}(X)$ is a strongly zero-dimensional space if and only if ${\beta}E_{cc}(X)$ and $S(\mathcal{G}(z_X))$ are homeomorphic. Using these, we show that $E_{cc}(X)$ is a strongly zero-dimensional space and $\mathcal{G}(z_X)=\mathcal{G}(X)$ if and only if ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권2호
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• pp.167-173
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• 2010

In this paper, we introduce the concept of a weakly P-space which is a generalization of a P-space and prove that for any covering map f : $X{\rightarrow}Y$, X is a weakly P-space if and only if Y is a weakly P-space. Using these, we investigate the minimal basically disconnected cover of weakly P-spaces and their products.

• 호남수학학술지
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• 제36권2호
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• pp.253-261
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• 2014

In this paper, we first will show that for any space X and any Wallman sublattice $\mathcal{A}$ of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}$, (${\Phi}^{-1}_{\mathcal{A}}(X)$, ${\Phi}_{\mathcal{A}}$) is the minimal quasi-F cover of X if and only if (${\Phi}^{-1}_{\mathcal{A}}(X)$, ${\Phi}_{\mathcal{A}}$) is a quasi-F cover of X and $\mathcal{A}{\subseteq}\mathcal{Q}_X$. Using this, if X is a locally weakly Lindel$\ddot{o}$f space, the set {$\mathcal{A}|\mathcal{A}$ is a Wallman sublattice of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}$ and ${\Phi}^{-1}_{\mathcal{A}}(X)$ is the minimal quasi-F cover of X}, when partially ordered by inclusion, has the minimal element $Z(X)^{\sharp}$ and the maximal element $\mathcal{Q}_X$. Finally, we will show that any Wallman sublattice $\mathcal{A}$ of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}{\subseteq}\mathcal{Q}_X$, ${\Phi}_{\mathcal{A}_X}:{\Phi}^{-1}_{\mathcal{A}}(X){\rightarrow}X$ is $z^{\sharp}$-irreducible if and only if $\mathcal{A}=\mathcal{Q}_X$.