• East Asian mathematical journal
• /
• v.34 no.3
• /
• pp.305-316
• /
• 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.

• Korean Journal of Mathematics
• /
• v.22 no.2
• /
• pp.217-234
• /
• 2014

Mason extended the reflexive property for subgroups to right ideals, and examined various connections between these and related concepts. A ring was usually called reflexive if the zero ideal satisfies the reflexive property. We here study this property skewed by ring endomorphisms, introducing the concept of an ${\alpha}$-skew reflexive ring, where is an endomorphism of a given ring.

• Kyungpook Mathematical Journal
• /
• v.46 no.4
• /
• pp.597-601
• /
• 2006

We introduce in this paper the concept of idempotent reflexive right ideals and concern with rings containing an injective maximal right ideal. Some known results for reflexive rings and right HI-rings can be extended to idempotent reflexive rings. As applications, we are able to give a new characterization of regular right self-injective rings with nonzero socle and extend a known result for right weakly regular rings.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.6
• /
• pp.1453-1461
• /
• 2023

Let R be a one-dimensional Noetherian domain with quotient field K and T be the integral closure of R in K. In this note we prove that if the conductor ideal (R :_K T) is a nonzero prime ideal, then every finitely generated reflexive (and hence finitely generated G-projective) R-module is isomorphic to a direct sum of some ideals.

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.257-264
• /
• 1992

Since Alfsen and Effors [1] introduced the notion of an M-ideal, many authors [3,6,9,12] have worked on the problem of finding those Banach spaces X and Y for which K(X,Y), the space of all compact linear operators from X to Y, is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y. The M-ideal property of K(X,Y) in L(X,Y) gives some informations on X,Y and K(X,Y). If K(X) (=K(X,X)) is an M-ideal in L(X) (=L(X,X)), then X has the metric compact approximation property [5] and X is an M-ideal in $X^{**}$ [10]. If X is reflexive and K(X) is an M-ideal in L(X), then K(X)$^{**}$ is isometrically isomorphic to L(X)[5]. A weaker notion is a semi M-ideal. Studies on Banach spaces X and Y for which K(X,Y) is a semi M-ideal in L(X,Y) were done by Lima [9, 10].

• Communications of the Korean Mathematical Society
• /
• v.24 no.2
• /
• pp.161-169
• /
• 2009

In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $\widehat{{\Gamma}_I(N)}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $\widehat{{\Gamma}_I(N)}$ are connected by a path of length at most 3, and if $\widehat{{\Gamma}_I(N)}$ contains a cycle, then the core K of $\widehat{{\Gamma}_I(N)}$ is a union of triangles and rectangles. We have shown that if $\widehat{{\Gamma}_I(N)}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.

• Journal of the Korean Society of Costume
• /
• v.43
• /
• pp.41-52
• /
• 1999

This study is to compare and analyze two types of 'transparency' concept expressed in architecture and garment which has not only been an important theme in the post-modern expression of architeture but been shown in various types of concept. This study examined the characteristics of transparency and through theoretical studies divided them into four types; frankness(purity ambiguity comparison exposure and eroticism) Purity building would use the matrial which is transparent glasses for the expprssion of its purity and clothing would use the transparent matrial for the expression of the natural beauty of human body and the purity of human of itself. Ambiguity is expressed in the outer side of architecture by duplicating transparent materials and by phenomenon of optical illusion and inflection. On the contrary in garment it is shown in the outward formation of underclothing. Comparison in architecture is expressed by the use of void but opaque materials as well as solid but transparent materials. Extinction is expressed with the visual effect of context of the surrounding by the use of opaque glass and reflexive glass. In garment the effect of comparison is expressed by the use of mixing transparent materials and opaque materials. Building would express the inside of itself by the way of its exposure and clothing would also express its frankness through the human body is partly opened or clossed at the same thime that arises from eroticism of the way of the expression of human feelings.

• Korean journal of communication and information
• /
• v.71
• /
• pp.157-193
• /
• 2015

The purpose of this study is to critically interpret generational trends in contemporary Korea through understanding the consumer experiences of luxury bag purchases of women in their late 20s and early 30s. Previous studies on luxury consumption tend to focus on an analysis of the value of luxury products as a sign and a symbol, the characteristics or class identity of luxury consumers, or expressive behavior in terms of ideal self-image. While including these factors, this study also expands the scope to a reflexive understanding of the social structural context behind the phenomenon of personal consumption. This was achieved by considering consumption in terms of the style and practice of everyday life, as well as its opportunities and limitations. In particular, we pay attention to how luxury bags are reproduced as media, which is a process that is circulated back to consumption, and through this process, this study reflects on capitalist life and subjects.

• Journal of Fisheries and Marine Sciences Education
• /
• v.13 no.1
• /
• pp.117-131
• /
• 2001

The character of the educational tradition of Germany could be divided into two aspects. One is the humanistic liberal tendency and the other is vocational. From the beginning of the Twentieth Century, however, there has been an attempt to unify these two trends by the . Georg Kerschensteiner is the first of importance to make some comprehensive curriculum for this goal. In Kerschensteiner, the genuine education makes the individual assume his work and role in society, and to develop them by cultivating insight, will and power. His view is well expressed in the slogn "The vocational education is the beginning of the humanistic education." His goal is to make men of independence and autonomy through vocational education. The theory of Kerschensteiner's education is called 'general vocational education'. The reason why is that his vocational education concerns not just technical training for industry, but also general liberal arts. In this point, Kerschensteiner's point of view goes back to Wilhelm von Humboldt, neo-humanist afar in the first half of the Ninteenth Century, and to John Dewey, pragmatist in the contemporary age of Kerschensteiner. Kerschensteiner was much influenced by Humboldt's concepts of power and individuality. These concepts came to be embodied as a principle of vocational education in Kerschensteiner. Furthermore, Humboldt's concept of power could be associated with Dewey's theory of reflexive thinking. The power in Humboldt is to create spirit, which is connected with the world outside through language. The reflexive thinking of Dewey is a process that examines and selects some alternative thinking in the consciousness before acting. This process makes one find the method of problem-solving which results in behaviour. That is the experimental spirit or pragmatic behaviourism. These theories are reduced to the concept of 'work' in Kerschensteiner. And Kerschensteiner's theory of education that has both sides, humanistic and vocational, is similar to that of John Dewey. Dewey brings forward the idea that the vocational education is the best way to cultivate intelligence and emotion, as intelligence operates best in the life. The position of Dewey is in accord with that of Kerschensteiner who intends to cover experiences of various fields of society through practice-learning, and to have knowledge got from outside of school, refuting the misled trend of education isolated from real life. However, there is some difference between Kerschensteiner and Humbolt or Dewey. While the Neo-humanism of Humbolt and the pragmatic education of Dewey put emphasis rather on the liberal arts and culture of individuality, Kerschensteiner is concerned more with the work and life of the reality of society as a group. Kerschensteiner's concept of utility is related to education for the whole man and to the work of the individual and the nation as well as the will and power to practice it. The ideal man of utility of Kerschensteiner is to learn perfectly the value and behaviour of society through vocational life and to have right view of the state establishing a sound mutual relation between individual and state. Kerschensteiner is regarded as a devotee of 'the state of harmony' or 'the ideal of the state', as he makes the state as the criterion for defining the role of the individual. It can be said that Kerschensteiner is not a democrat of the American style as Dewey is, as he makes much of the value of the nation and state. However, he is a humanist and democrat in the point of vocational education. His purpose of education is to make whole men through work and vocational education.