• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1733-1757
• /
• 2017

Let $R={\oplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be an integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$, ${\bar{R}}$ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of $f{\in}R_H$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. Let $R_H$ be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if $Q=fR_H{\cap}R$ for some $f{\in}R$ and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of $R_{N(H)}$ is extended from a homogeneous ideal of R, if and only if ${\bar{R}}_{H{\backslash}Q}$ is a graded-$Pr{\ddot{u}}fer$ domain for all homogeneous maximal t-ideals Q of R, if and only if ${\bar{R}}_{N(H)}$ is a $Pr{\ddot{u}}fer$ domain, if and only if R is a UMT-domain.

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.265-275
• /
• 1992

The characteristic free representation theory of the general linear group has found a wide range of applications, ranging from the theory of free resolutions to the symmetric function theory. Representation theory is used to facilitate the calculation of explicit free resolutions of large classes of ideals (and modules). Recently, K. Akin and D. A. Buchsbaum [2] realized the Jacobi-Trudi identity for a Schur function as a resolution of GL$_{n}$-modules. Over a field of characteristic zero, it was observed by A. Lascoux [6]. T.Jozefiak and J.Weyman [5] used the Koszul complex to realize a formula of D.E. Littlewood as a resolution of schur modules. This leads us to further study resolutions of Schur modules of a particular form. In this article we will describe some new classes of finite free resolutions associated to the Pieri type skew Young diagrams. As a special case of these finite free resolutions we obtain the generalized Koszul complex constructed in [1]. In section 2 we review some of the basic difinitions and properties of Schur modules that we shall use. In section 3 we describe certain exact complexes associated to the Pieri type skew partitions. Throughout this article, unless otherwise specified, R is a commutative ring with an identity element and a mudule F is a finitely generated free R-module.e.

• Journal of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.85-98
• /
• 2012

Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(${\Gamma}_I(R)$). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y ${\in}$ R, the vertices x and y are adjacent if and only if x + y ${\in}$ S(I). The total graph of a commutative ring, that denoted by T(${\Gamma}(R)$), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y ${\in}$ Z(R) which is due to Anderson and Badawi [2]. In the case I = {0}, $T({\Gamma}_I(R))=T({\Gamma}(R))$; this is an important result on the definition.

• Journal of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.853-866
• /
• 2014

Constacyclic codes of length $p^s$ over $R=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}$ are precisely the ideals of the ring $\frac{R[x]}{<x^{p^s}-1>}$. In this paper, we investigate constacyclic codes of length $p^s$ over R. The units of the ring R are of the forms ${\gamma}$, ${\alpha}+u{\beta}$, ${\alpha}+u{\beta}+u^2{\gamma}$ and ${\alpha}+u^2{\gamma}$, where ${\alpha}$, ${\beta}$ and ${\gamma}$ are nonzero elements of $\mathbb{F}_{p^m}$. We obtain the structures and Hamming distances of all (${\alpha}+u{\beta}$)-constacyclic codes and (${\alpha}+u{\beta}+u^2{\gamma}$)-constacyclic codes of length $p^s$ over R. Furthermore, we classify all cyclic codes of length $p^s$ over R, and by using the ring isomorphism we characterize ${\gamma}$-constacyclic codes of length $p^s$ over R.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.17 no.7
• /
• pp.1531-1537
• /
• 2013

In its change in ICT Ecosystem, electronic government changes to its wireless m-Gov from existing PC-based e-Gov. Thus, in order to realize the smart government, m-Gov needs to be vitalized and the strategies for this realization are required. Also, some countermeasures for those strategies and political instructions which the electric government should follows are needed. Above two are the ultimate purpose in pursuing administrative ideals because the realization of m-Gov innovates the government and betters quality of national life off. Therefore, this paper, to realize the smart government, provides some strategies for vitalization of m-Gov's electric government services, their countermeasures, and political instructions for Smart m-Gov.

• The Journal of the Convergence on Culture Technology
• /
• v.2 no.1
• /
• pp.45-51
• /
• 2016

Aristotle said 'Poet is that from who can give happiness, therapeutic effects to the reader.' He say to 'mimoumenon' it means a native Image restored. However, Kant said that Aesthetic is requested not only reappearance but freedom. This result is that between joyful freedom and reason of the judgement of tasted feeling. Because Art ever created is the spirit of the moral ideals, and those who combine the best of the joy. I think need to more communication and joy than their theories. For poet is replaced to be communicated and joyful for our happiness and freedom.

• Korean Journal of Mathematics
• /
• v.7 no.2
• /
• pp.227-233
• /
• 1999

Let $k$ be a real abelian field and $k_{\infty}={\bigcup}_{n{\geq}0}k_n$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. For each $n{\geq}0$, we denote the class number of $k_n$ by $h_n$. The following is a well known theorem: Theorem. Suppose $p$ remains inert in $k$ and the prime ideal of $k$ above $p$ totally ramifies in $k_{\infty}$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$. The aim of this paper is to generalize above theorem: Theorem 1. Suppose $H^1(G_n,E_n){\simeq}(\mathbb{Z}/p^n\mathbb{Z})^l$, where $l$ is the number of prime ideals of $k$ above $p$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$. Theorem 2. Let $k$ be a real quadratic field. Suppose that $H^1(G_1,E_1){\simeq}(\mathbb{Z}/p\mathbb{Z})^l$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$.

• Fashion & Textile Research Journal
• /
• v.22 no.1
• /
• pp.1-10
• /
• 2020

Romanticists realized the ideals of a more fantastic and better society for the present day in which they lived; in addition, dress was an important medium of expression of this period. The Incroyables were a group that expressed eccentric forms and abuses of luxury through their clothing, centering around the second generation of financial elite groups during the French Directoire. Incroyables created their own fashion that expresses their new image in dress, expressing the intense personal innerity of life, which was influenced by the romanticism of pursuing an internal expression of the subjective and emotional individual. This study used a literature review to analyze the characteristics of the Romanticism expressed in the Incroyables fashion. The research results were as follows. First, it was an expression of an emotional desire for and ancient regime. Incroyables fashion were based on bourgeois nostalgia for the days of the ancient regime that resulted in an emphasis on individual and original human views. Second, it was also a hybrid of Romantic classicism. It was a form emphasizing body form where body beauty expressed a classical form through a dress under the influence of neo-classicalism that desires to return to nature.

• Kyungpook Mathematical Journal
• /
• v.55 no.2
• /
• pp.289-300
• /
• 2015

In [9], the author extends the definition of lifting and supplemented modules to ${\delta}$-lifting and ${\delta}$-supplemented by replacing "small submodule" with "${\delta}$-small submodule" introduced by Zhou in [13]. The aim of this paper is to show new properties of ${\delta}$-lifting and ${\delta}$-supplemented modules. Especially, we show that any finite direct sum of ${\delta}$-hollow modules is ${\delta}$-supplemented. On the other hand, the notion of amply ${\delta}$-supplemented modules is studied as a generalization of amply supplemented modules and several properties of these modules are given. We also prove that a module M is Artinian if and only if M is amply ${\delta}$-supplemented and satisfies Descending Chain Condition (DCC) on ${\delta}$-supplemented modules and on ${\delta}$-small submodules. Finally, we obtain the following result: a ring R is right Artinian if and only if R is a ${\delta}$-semiperfect ring which satisfies DCC on ${\delta}$-small right ideals of R.

• Journal of Contemporary Eastern Asia
• /
• v.4 no.1
• /
• pp.1-7
• /
• 2005

In this paper uses Kaname Akamatsu's 'Flying Geese' model to analyse Japan's role in East Asian integration. Japan made the first attempt to lead Asian countries before the Second World War. At that time, the Japanese Government embarked on a brutally expansionist policy the result of which was creation of the first gaggle of 'flying geese' under the name of the 'Greater East Asia Co-Prosperity Sphere.' During the 'flight' Japan was forcefully imposing its own ideals and values on the rest of the 'gaggle.' At the same time, the Japanese Government assumed hostile attitude toward Western countries. Japan's defeat in the Second World War signified the end of flight for the first 'flying geese' gaggle. After the war, Japan made another attempt at regional integration. This time it was done through establishing a production network in East Asia. Thus the second gaggle of 'flying geese' came into existence. During the flight of the 'second gaggle' of geese, Japan was fostering good ties with Western countries as well, especially the United States. However, some leaders of the 'second gaggle's' member-countries emboldened by their countries' economic success proclaimed that future belongs to Asia and put forward the 'Asian values' argument. The Asian economic crisis of 1997 interrupted the flight of the 'second gaggle' and effectively put an end to the 'Asian values' debate. It is interesting to note that some elements of the 'Asian values' argument resembled ultranationalist discourse that had been dominant in Japan before and during the Second World War. This paper compares historical patterns of East Asian regional integration and highlights future challenges for Japan's Asia policy.