• Title/Summary/Keyword: right ideals

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ARCHIMEDEAN SKEW GENERALIZED POWER SERIES RINGS

  • Moussavi, Ahmad;Padashnik, Farzad;Paykan, Kamal
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.361-374
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    • 2019
  • Let R be a ring, ($S,{\leq}$) a strictly ordered monoid, and ${\omega}:S{\rightarrow}End(R)$ a monoid homomorphism. In [18], Mazurek, and Ziembowski investigated when the skew generalized power series ring $R[[S,{\omega}]]$ is a domain satisfying the ascending chain condition on principal left (resp. right) ideals. Following [18], we obtain necessary and sufficient conditions on R, S and ${\omega}$ such that the skew generalized power series ring $R[[S,{\omega}]]$ is a right or left Archimedean domain. As particular cases of our general results we obtain new theorems on the ring of arithmetical functions and the ring of generalized power series. Our results extend and unify many existing results.

RINGS WITH REFLEXIVE IDEALS

  • Han, Juncheol;Park, Sangwon
    • East Asian mathematical journal
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    • v.34 no.3
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    • pp.305-316
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    • 2018
  • Let R be a ring with identity. A right ideal ideal I of a ring R is called ref lexive (resp. completely ref lexive) if $aRb{\subseteq}I$ implies that $bRa{\subseteq}I$ (resp. if $ab{\subseteq}I$ implies that $ba{\subseteq}I$) for any $a,\;b{\in}R$. R is called ref lexive (resp. completely ref lexive) if the zero ideal of R is a reflexive ideal (resp. a completely reflexive ideal). Let K(R) (called the ref lexive radical of R) be the intersection of all reflexive ideals of R. In this paper, the following are investigated: (1) Some equivalent conditions on an reflexive ideal of a ring are obtained; (2) reflexive (resp. completely reflexive) property is Morita invariant; (3) For any ring R, we have $K(M_n(R))=M_n(K(R))$ where $M_n(R)$ is the ring of all n by n matrices over R; (4) For a ring R, we have $K(R)[x]{\subseteq}K(R[x])$; in particular, if R is quasi-Armendaritz, then R is reflexive if and only if R[x] is reflexive.

Some Results on δ-Semiperfect Rings and δ-Supplemented Modules

  • ABDIOGLU, CIHAT;SAHINKAYA, SERAP
    • Kyungpook Mathematical Journal
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    • v.55 no.2
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    • pp.289-300
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    • 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.

ON LIFTING OF STABLE RANGE ONE ELEMENTS

  • Altun-Ozarslan, Meltem;Ozcan, Ayse Cigdem
    • Journal of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.793-807
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    • 2020
  • Stable range of rings is a unifying concept for problems related to the substitution and cancellation of modules. The newly appeared element-wise setting for the simplest case of stable range one is tempting to study the lifting property modulo ideals. We study the lifting of elements having (idempotent) stable range one from a quotient of a ring R modulo a two-sided ideal I by providing several examples and investigating the relations with other lifting properties, including lifting idempotents, lifting units, and lifting of von Neumann regular elements. In the case where the ring R is a left or a right duo ring, we show that stable range one elements lift modulo every two-sided ideal if and only if R is a ring with stable range one. Under a mild assumption, we further prove that the lifting of elements having idempotent stable range one implies the lifting of von Neumann regular elements.

Data Protection and Privacy over the Internet: Towards Development of an International Standard (온라인 정보보호 및 프라이버시에 관한 국제 표준 개발)

  • Zoo, Hanah;Lee, Heejin;Kwak, Jooyoung;Kim, Yong-Young
    • Journal of Digital Convergence
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    • v.11 no.4
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    • pp.57-69
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    • 2013
  • Progresses in ICT make the processing and exchange of personal data across international borders often necessary and relatively easy. The challenge lies in protecting fundamental rights and freedoms of individuals, notably the right to privacy and the right to personal information, while encouraging the free and secure flow of information across borders for the continued expansion of online transactions. The key to establishing a functioning international solution for personal data protection is to strike a right balance between the two camps which currently dominate the debate - the advocates of individual privacy rights on one side exemplified by the EU, and the proponents of self-regulation and economic efficiency on the other, represented by the U.S. In the face of a growing tension between the two sides each equipped with their own ideals, a practical solution may lie in utilizing established institutions of standardization such as ISO and IEC as a ground upon which an agreement can take its root.

A Study on the Theories of Ideal Society in Daesoonjinrihoe (대순진리회의 이상사회론 연구)

  • Na, Kwon-soo
    • Journal of the Daesoon Academy of Sciences
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    • v.21
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    • pp.409-452
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    • 2013
  • This paper aims to cast light on the theoretical characteristics of Korean new religions' utopian theory from the perspective of theology and apply the findings to the utopian theory of the new religions in Korea. The utopian theory of the new religions in Korea occurred to meet people's aspiration towards a new world on the background of the national ordeal and its consequential psychology in the late Chosun dynasty. As a result, it has the characteristics of a shift from a pure religious framework to participation in reality to realize religious ideals 'right here, right now'. Thus, it basically defined an utopian theory as the product of a society and history, and explained the utopian theory as the projection of the thoughts about current conflicts. However, an approach in this way may leave the likelihood that the individual characteristics of Daesoonjinrihoe would be overlooked and the utopian theory would be limited to the byproduct of the age, only. Thus, this paper has dealt with the religious experience of the founders as the lead of discussion, not a sociological approach. In this context, the religious experience of founders can be more significant clues to view the characteristics of an utopian theory. This directivity of a study can be understood as an attempt to improve the previous sociological methodologies, the leading discourses, and to contribute to the different perspectives on an understanding of the utopian theories of Daesoonjinrihoe. Furthermore, this paper is anticipated to give salience to the individual characteristics reflected in the new religions in Korea and to enhance its status in the history of thoughts, not as the trend of the thought limited to the past.

Democracy, leadership and political culture in Korea: With specific focus on political efficacy and trust (한국의 민주주의, 리더십과 정치문화: 정치효능감과 신뢰를 중심으로)

  • Uichol Kim
    • Korean Journal of Culture and Social Issue
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    • v.8 no.2
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    • pp.137-170
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    • 2002
  • The present paper reviews the development of democracy in the West and Korea. The first part of the paper provide a cultural framework for understanding the development of democracy in West and Korea. In the second part of the paper, an empirical study conducted in Korea will be presented. A survey questionnaire was developed to assess respondents' conception of political participation, political efficacy, trust, leadership, and social relations and it has been administered to national stratified sample in Korea (n=1,000). The results indicate that Korean respondents support the basic ideas of liberal democracy, such as the right to vote, participate in political organization, freedom of speech, and criticize government. At the same time, Korean respondents supported collective values, such as harmonious family life, harmonious social relations, and governmental welfare programs. Although Koreans trusted close ingroup members, such as family members and friends, they were less likely to trust their colleagues and outgroup members and were not likely to trust political and governmental institutions. Moreover, Korean respondents showed a low degree of political participation and efficacy and a high degree of political alienation. As for leadership, Koreans preferred moral and strong leaders. The overall results indicate that in Korea, although the basic ideals of democracy are valued, the method of implementing these ideals is different from the West. Detailed analysis of the results and implications of the study will be presented.

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Group Creativity and Creative Environment by Gender of University Students (대학생의 성별에 따른 집단창의성과 창의적 환경)

  • Lew, Kyoung-Hoon
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.16 no.12
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    • pp.8416-8423
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    • 2015
  • The purpose of this study was to find out early childhood teachers' personality and analysis on the status and awareness of character education for early childhood education by grouping according to level of personality. The results show that there was significantly difference career and age. While early childhood teachers sympathize importance and need of personality education, absence of methods for practice is obstacle. A high level personality group notices that respect for early children' life, humanity and virtue of relationship is importance virtue. Therefore they consider respecting people as aim of personality education and recognize that they need to teach right values through whole area as education contents. A low level personality group notices that performance of their duty and manners of early children is needed virtue. They consider manners education as aim and content of personality education also recognize guiding with connecting home teaching is desirable. Early childhood teachers recognize that ambiguity of personality education's aim and contents, a gap between reality and ideals and absence of teachers' personality is difficulty of personality education.

A Biographical Study of Social Exclusion Experiences - Focused on the Physical and Cerebral Palsy Disabled - (장애인의 사회적 배제 경험에 대한 생애사 연구 -지체와 뇌병변 장애인 중심으로-)

  • Shin, Yu-Ri
    • Korean Journal of Social Welfare
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    • v.64 no.2
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    • pp.299-323
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    • 2012
  • The purpose of this study is to understand social exclusion experiences with the disabled through a biographical study. It is analysed the interview date conducting an interview about 10 focused on the physical and cerebral palsy disabled with social exclusion experiences. The results show that it is multi-social exclusion including the inequality of approach opportunity of education, labor, education, medical, social participation, information, social service, space, health etc. It shows their life neglected and marginalized resulted from not providing social right as citizenship. And their social relationship is isolated by social exclusion and Other-directed identity is to be shaped in accordance to the method to define as regulated social ideals. Also, there is their painful and heavy life bound with double risky factors of disability and poverty. They share common historical experiences and social events impacted on their recognition and value among participants generation in biographical narrative. On the other hand, their life is reconstructed according to each their resource and standard to interpreter and evaluate on it. It suggests political and clinical implications in order to overcome the disabled's social exclusion, which is based on practical and vivid experiential dates from the participants.

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Jeongjo's Enjoyment of the Palace Garden (정조(正祖)의 궁원(宮苑) 유락(遊樂))

  • Hong, Hyoung-Soon
    • Journal of the Korean Institute of Traditional Landscape Architecture
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    • v.33 no.4
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    • pp.10-25
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    • 2015
  • The purpose of this research is to investigate the reality behind Jeongjo's enjoyment of the palace garden. If I were to summarize the results of this research, they are as follows: First, The 'Sanghwajoeoyeon(賞花釣魚宴)' has the differentiation which decided and regularized the rules and the regulations with the annual meetings for the Kyujanggak(奎章閣). Jeongjo had held the events five times. Second, The 'Seshimdae(洗心臺) Excursion' is based on the tragic personal history of Jeongjo. There were four events. Third, Jeongjo had enjoyed the 'viewing of the waterfall(觀瀑)' of the Okryucheon(玉流川) where a lot of the water overflows right after it rains. This is worth the special mention with regard to the point that it is a temporary landscape and not an usual landscape. Fourth, As an event for the military officers, the 'Seoljungryonghohwe(雪中龍虎會)' was held seven times. This event had been held in the middle of the winter. And each of the attendees skewered a pheasant and roasted and ate it. Also, it emphasized the sovereign and the subjects being the partners of the joys and the sorrows by giving the alcoholic drinks and the music. Fifth, Jeongjo had consoled the hard work by the civilian subjects either by holding the brazier feast(煖爐會) in the winter or by granting the alcoholic drinks and the foods according to the historical facts of the brazier feasts. Sixth, Jeongjo was good at archery and enjoyed it. During the period of his reign, Jeongjo held twice Yeonsarye(燕射禮). Seventh, Jeongjo soothed his desire to get out of the busy everyday life at the royal palace garden. While appreciating the natural landscape of the backyard, he was awakened of the meaning of the Book of Changes(周易) in which all the things had been created and changed. Eighth, At the royal palace garden, Jeongjo actively prepared the place for enjoyment by the sovereign and the subjects together. It is judged that this is because, in order to materialize his political ideals, the support by all the subjects who had been close was needed. The limitation of this research is the fact that the research had been proceeded with limited to the translations, among the many old writings related to Jeongjo. With the accumulation of the excavations of the new thoughts and of the results of the translations, the researches that are deeper will be needed.