• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.33-39
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• 1994

The purpose of this paper prove the following property; Suppose A has many units (local global ring) and |A/m| > 5 for every maximal ideal $m{\subseteq}A$. Let(E, q) ${\in}$ Q(A) and $E=E_1{\bot}{\cdots}{\bot}E_t$ be an orthogonl decomposition of E with $t{\geq}2$ and $rk(E_i){\geq}1$, for $i=1,{\cdots},t$. Let $x{\in}E$ be a primitive vector. Then there exists ${\sigma}{\in}O(q)$ such that ${\sigma}(x)$ is transversal to this decomposition.

• 한국IT서비스학회:학술대회논문집
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• 2009.05a
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• pp.205-208
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• 2009

이 논문에서는 RFID(Radio Frequency IDentification)에 대한 여러 가지 보안위협에 대하여 간단히 알아보고 그에 대응하는 안전한 암호학적 도구(Primitive)에 대하여 알아보겠다. 공개키 암호시스템(PKC, Public Key Cryptosystem)에 사용되는 타원곡선(EC, Elliptic Curve) 암호, NTRU(N-th degree TRUncated polynomial ring) 암호, Rabin 암호 등은 초경량 하드웨어 구현에 적합한 차세대 암호시스템으로서 안전한 RFID 인증서비스 제공과 프라이버시보호를 가능케 한다. 특히, 본고에서는 초경량 키의 길이, 저전력 소모성, 고속구현 속도를 갖는 타원곡선암호의 안전성에 대한 가이드라인을 제공하겠다.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.309-326
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• 2021

In near-ring theory several different types of primitivity exist. These all imply several different types of primeness. In case of near-rings with DCCN most of the types of primeness are known to imply primitivity of a certain kind. We are able to show that also so called 1-prime near-rings imply 1-primitivity. This enables us to classify maximal ideals in near-rings with chain condition with the concept of 1-primeness which leads to further results in the structure theory of near-rings.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.45-49
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• 1983

If R is ring and M is a right (or left) R-module, then M is called a faithful R-module if, for some a in R, x.a=0 for all x.mem.M then a=0. In [4], R.E. Johnson defines that M is a prime module if every non-zero submodule of M is faithful. Let us define that M is of prime type provided that M is faithful if and only if every non-zero submodule is faithful. We call a right (left) ideal I of R is of prime type if R/I is of prime type as a R-module. This is equivalent to the condition that if xRy.subeq.I then either x.mem.I ro y.mem.I (see [5:3:1]). It is easy to see that in case R is a commutative ring then a right or left ideal of a prime type is just a prime ideal. We have defined in [5], that a chain of right ideals of prime type in a ring R is a finite strictly increasing sequence I$_{0}$.contnd.I$_{1}$.contnd....contnd.I$_{n}$; the length of the chain is n. By the right dimension of a ring R, which is denoted by dim, R, we mean the supremum of the length of all chains of right ideals of prime type in R. It is an integer .geq.0 or .inf.. The left dimension of R, which is denoted by dim$_{l}$ R is similarly defined. It was shown in [5], that dim$_{r}$R=0 if and only if dim$_{l}$ R=0 if and only if R modulo the prime radical is a strongly regular ring. By "a strongly regular ring", we mean that for every a in R there is x in R such that axa=a=a$^{2}$x. It was also shown that R is a simple ring if and only if every right ideal is of prime type if and only if every left ideal is of prime type. In case, R is a (right or left) primitive ring then dim$_{r}$R=n if and only if dim$_{l}$ R=n if and only if R.iden.D$_{n+1}$ , n+1 by n+1 matrix ring on a division ring D. in this paper, we establish the following results: (1) If R is prime ring and dim$_{r}$R=n then either R is a righe Ore domain such that every non-zero right ideal of a prime type contains a non-zero minimal prime ideal or the classical ring of ritght quotients is isomorphic to m*m matrix ring over a division ring where m.leq.n+1. (b) If R is prime ring and dim$_{r}$R=n then dim$_{l}$ R=n if dim$_{l}$ R=n if dim$_{l}$ R<.inf. (c) Let R be a principal right and left ideal domain. If dim$_{r}$R=1 then R is an unique factorization domain.TEX>R=1 then R is an unique factorization domain.

• Journal of Plant Biology
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• v.34 no.1
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• pp.67-75
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• 1991

Anatomical study of the secondary xylem in Malvales plants, including four families, five genera and ten species grown in Korea, was carried out to elucidate relationship among genera or families in the order. Wood of Elaeocarpus is diffuse porous and shows angular vessels in radial multiples of 2-14 cells and a few apotracheal or paratracheal parenchyma. Tiliaceous genera have diffuse porous wood, vessels in solitary distribution and apotracheal parenchyma of sinuous scalariform uniseriate band. In the family, Tilia shows angular vessel. noded and tile-like cell in ray and storied tissue but Grewia has circular vessel. Hibiscus shows ring porous wood, circular solitary vessel and biseriate band of apotracheal and paratracheal parenchyma. Firmiana shows ring porous wood, circular solitary vessel and confluent parenchyma. Many starch grains appear in ray and axial parenchyma. Judging from arrangement, shape, length and diameter of vessel element and angle of end wall to vessel axis, and arrangement and shape of axial parenchyma, the lines of specialization in these genera are from primitive Elaeocarpaceae through less primitive Tiliaceae and less advanced Malvaceae to advanced Sterculiaceae.iaceae.

• The Journal of the Petrological Society of Korea
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• v.10 no.1
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• pp.13-26
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• 2001

Songaksan volcano, which occurs as a monogenetic volcano on the southwestern promontory of Hallasan shield volcano, is composed of tuff ring, cinder cone, lava pond and cinder conelet complex on wide basalt plateau. Except for an influx of external quartz xenocrysts in the tuff ring. Totally the volcano ranges from trachyandesite to trachybasalt in petrography and chemical compositions, which confirm the continuum between the evolved and primitive compositions widely occurring in the Jeju volcanic system. Chemical data for the volcano show quantitative compositional variation from the lower to the upper part of the volcanic sequences. The continuous compositional variations generally define a compositionally zoned magma storage. The chemical data suggest that the compositiona1 donations might have resulted from the fractional crystallization of a parental alkali magma. As result, the Songaksan volcano initially tapped the lop of the zoned magma storage and subsequently erupted successively more primitive magma.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1281-1299
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• 2017

A submodule N of a module M is called ${\mathcal{S}}$-closed (in M) if M/N is nonsingular. It is well-known that the class Closed of short exact sequences determined by closed submodules is a proper class in the sense of Buchsbaum. However, the class $\mathcal{S}-Closed$ of short exact sequences determined by $\mathcal{S}$-closed submodules need not be a proper class. In the first part of the paper, we describe the smallest proper class ${\langle}\mathcal{S-Closed}{\rangle}$ containing $\mathcal{S-Closed}$ in terms of $\mathcal{S}$-closed submodules. We show that this class coincides with the proper classes projectively generated by Goldie torsion modules and coprojectively generated by nonsingular modules. Moreover, for a right nonsingular ring R, it coincides with the proper class generated by neat submodules if and only if R is a right SI-ring. In abelian groups, the elements of this class are exactly torsionsplitting. In the second part, coprojective modules of this class which we call ec-flat modules are also investigated. We prove that injective modules are ec-flat if and only if each injective hull of a Goldie torsion module is projective if and only if every Goldie torsion module embeds in a projective module. For a left Noetherian right nonsingular ring R of which the identity element is a sum of orthogonal primitive idempotents, we prove that the class ${\langle}\mathcal{S-Closed}{\rangle}$ coincides with the class of pure-exact sequences of modules if and only if R is a two-sided hereditary, two-sided $\mathcal{CS}$-ring and every singular right module is a direct sum of finitely presented modules.

• Bulletin of the Korean Chemical Society
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• v.29 no.8
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• pp.1485-1490
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• 2008

Dumbbell-shaped aromatic amphiphilic molecules consisting of a dodeca-p-phenylene as a rigid segment and oligoether dendrons as a flexible chains were synthesized, characterized, and their aggregation behavior was investigated in the bulk and at the air-water interface. In contrast to the molecule 2 which shows a nematic liquid crystalline state, molecule 1 based on shorter dendritic chains was observed to self-assemble into a 3-D primitive orthorhombic supercrystal. And molecule 1 at the air-water interface was observed to reorganize from circular plates to ring structures by lateral compressions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.339-348
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• 2023

It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R₁ × R₂, where R₁, R₂ are rings which satisfy R₁ is a semi-simple Artinian ring and R₂ is square-free as a right R₂-module and all idempotents of R₂ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

• Applied Microscopy
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• v.29 no.3
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• pp.281-289
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• 1999

The stirred and thixoformed $SiC_p/AZ91HP$ Mg composites are studied on the basis of microstructural analysis using transmission electron microscopy (TEM). The products of interfacial reaction are identified as $Mg_2Si$, MgO and $Mg_{17}Al_{12}$ phases and the crystallized phases are found to be orthorhmbic $Al_6Mn$ and decagonal T phases. It is shown that $Mg_2Si$ and $Mg_{17}Al_{12}$ phases are found at the surface of $SiC_p$ and $Al_6Mn$ is found near interface and crystallized on the matrix. Phase identification is carried out by crystallographic work based on primitive cell volume, zero order Laue zone (ZOLZ) patterns and single convergent beam electron diffraction (CBED) patterns containing higher order Laue zone ring from a nanosized region.