• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1117-1123
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• 2001

A ring is a DICC ring if every chain of right ideals in-dexed by the integers stabilizes to the left or to the right or to both sides. A counterexample is given to an assertion of karamzadeh and Motamedi that a transfinite power of the Jacobson radical of a right DICC ring is zero. we determine the behavior of the transfinite powers of the Jacobson radical relative to a torsion theory and consequently can obtain their correct behavior in the classical setting.

• Journal for History of Mathematics
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• v.16 no.3
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• pp.89-94
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• 2003

Though the concept of unique factorization was formulated in tile 19th century, Euclid already had considered the prime factorization of natural numbers, so called tile fundamental theorem of arithmetic. The unique factorization of algebraic integers was a crucial problem in solving elliptic equations and the Fermat Last Problem in tile 19th century On the other hand the unique factorization of the formal power series ring were a critical problem in the past century. Unique factorization is one of the idealistic condition in computation and prime elements and prime ideals are vital ingredients in thinking and solving problems.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1957-1972
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• 2013

The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. In this note we study the structure of idempotents satisfying the reflexive property and introduce reflexive-idempotents-property (simply, RIP) as a generalization. It is proved that the RIP can go up to polynomial rings, power series rings, and Dorroh extensions. The structure of non-Abelian RIP rings of minimal order (with or without identity) is completely investigated.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1267-1279
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• 2007

For a ring endomorphism ${\alpha}$ and an ${\alpha}-derivation\;{\delta}$ of a ring R, we study relation between the set of annihilators in R and the set of annihilators in nearring $R[x;{\alpha},{\delta}]\;and\;R_0[[x;{\alpha}]]$. Also we extend results of Armendariz on the Baer and p.p. conditions in a polynomial ring to certain analogous annihilator conditions in a nearring of skew polynomials. These results are somewhat surprising since, in contrast to the skew polynomial ring and skew power series case, the nearring of skew polynomials and skew power series have substitution for its "multiplication" operation.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1251-1267
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• 2014

The semicommutative property of rings was introduced initially by Bell, and has done important roles in noncommutative ring theory. This concept was generalized to one of nil-semicommutative by Chen. We first study some basic properties of nil-semicommutative rings. We next investigate the structure of Ore extensions when upper nilradicals are ${\sigma}$-rigid ${\delta}$-ideals, examining the nil-semicommutative ring property of Ore extensions and skew power series rings, where ${\sigma}$ is a ring endomorphism and ${\delta}$ is a ${\sigma}$-derivation.

• The Research Journal of the Costume Culture
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• v.31 no.5
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• pp.573-585
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• 2023

Comprehending the prevailing ideals of the body within a specific era requires grasping the intricate interplay between social phenomena and the evolution of clothing. Accordingly, this study investigates the distinctive facets of the perception of the Neo-Confucian body as reflected in men's dress during the Joseon Dynasty. We examine a comprehensive body of scholarship, literature, and historical records concerning the body and dress. Additionally, we also employ a framework developed by M. Y. Kim, which categorizes the Neo-Confucian body in three ways: as the natural body, the cultural body, and the body as a fully-realized moral subject. Our findings unveil three crucial insights: firstly, guided by Neo-Confucian discourse positing appearance as a manifestation of innate energy (氣), men's dress was deliberately designed to demarcate stylistic distinctions in women's dress; secondly, the Chinese gwan (冠) was employed as a tool of self-cultivation (修身) to symbolize the legitimacy of Joseon's Neo-Confucian governance; and thirdly, sim-ui (深衣), a philosophical emblem of Confucianism extensively represented across through an intensified exploration of historical sources, served as a means to consolidate the political standing of the Neo-Confucian faction. As a consequence of these factors, the attire of noble men conferred upon them both sexual and moral ascendancy as political entities; men's dress became a visual manifestation of the legitimacy of their power, thus embodying Neo-Confucian ideals. This study carries significance by applying a discourse analysis approach to Korean dress research and elucidating the factors underlying the development of men's dress during the Joseon Dynasty.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.397-408
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• 2016

Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If $d(uv)^n=d(u)^md(v)^l$ or $d(uv)^n=d(v)^ld(u)^m$ for all $u,v{\in}L$, where m, n, l are xed positive integers, then $L{\subseteq}Z$. We also examine the case when R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on non-commutative Banach algebras. This result simultaneously generalizes a number of results in the literature.

• Honam Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 2006

A scheme based on the cryptography for enforcing multilevel security in a system where hierarchy is represented by a partially ordered set was first introduced by Akl et al. But the key generation algorithm of Akl et al. is infeasible when there is a large number of users. In 1985, MacKinnon et al. proposed a paper containing a condition which prevents cooperative attacks and optimizes the assignment in order to overcome this shortage. In 2005, Kim et al. proposed key management systems for multilevel security using one-way hash function, RSA algorithm, Poset dimension and Clifford semigroup in the context of modern cryptography. In particular, the key management system using Clifford semigroup of imaginary quadratic non-maximal orders is based on the fact that the computation of a key ideal $K_0$ from an ideal $EK_0$ seems to be difficult unless E is equivalent to O. We, in this paper, show that computing preimages under the bonding homomorphism is not difficult, and that the multilevel cryptosystem based on the Clifford semigroup is insecure and improper to the key management system.

• Journal of Fashion Business
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• v.4 no.3
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• pp.67-78
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• 2000

This is a study on the art style of amimal fight in Scytian ornaments which had been popular in Steppe region of Eurasia. Animals were considered to have magical power and to provide protection against evil or disaster and representations of them thus occupied an important place in life. This style reflected the mythology, the ethical and aesthetic ideals of the warrior-nomad. With a magnificent understanding of composition and the essential nature of the material, craftsmen fashioned utilitarian objects in animal form: weaponry, horse trappings, clothes, ornaments and jewellery and other everyday objects were all decorated with zoomorphic motifs. Without copying nature, they accurately conveyed the essence of every beast depicted. The highly stylized modelling uses bold accentuated planes, while distinctive features associated with particular species are emphasized and exaggerated. The purpose and meaning of the animal motifs used in Scythian ornaments appears that in some cases the work was intended to be purely ornamental, while many times the motifs had symbolic meaning (such as the successful dominance of the aggressor over the victim portrayed in the attack scenes). Magical use of symbols may have been intended to guarantee the power of the aggressor.

• International Journal of Costume and Fashion
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• v.15 no.1
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• pp.39-49
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• 2015

Heavenly Kingdom was known for their strict discipline and law as well as their anti-corruption practices and for putting up unconventional ideas to rule its kingdom. They became weak as their leadership was split along with the power struggles that occurred within their kingdom. Heavenly Kingdom's style of dress also ended during this period, but their philosophy continues to influence the style of dress. Taiping rebellion was modern China's biggest internal disturbance which prior studies included political ideals, gender equality and the peasant movement. My research is to associate Heavenly Kingdom's ideas and their dress style by analyzing its relations. Their form of clothing was similar to the Qing Dynasty but the same. They wanted to restore their identity of the Han(漢) while their ideology was oriented in creating a large enough military power to go against the corrupt Qing Dynasty as seen in their military uniform. This research is to analyze about Heavenly Kingdom's ideology with regard to their style of dress but because of their short existence, there are only small remains of artifacts and clothing available which limits this research. This research has to developing further research as I gather more additional data.