• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.1
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• pp.181-194
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• 2013

Landslides are known as gravitational mass movements that can carry the flow materials ranging in size from clay to boulders. The various types of landslides are differentiated by rate and depositional features. Indeed, flow characteristics are observed from very slow-moving landslides (e.g., mud slide and mud flow) to very fast-moving landslides (e.g., debris avalanches and debris flows). From a geomechanical point of view, shear-rate-dependent shear strength should be examined in landslides. This paper presents the design of advanced ring-shear apparatus to measure the undrained shear strength of debris flow materials in Korea. As updated from conventional ring-shear apparatus, this apparatus can evaluate the shear strength under different conditions of saturation, drainage and consolidation. We also briefly discussed on the ring shear apparatus for enforcing sealing and rotation control. For the materials with sands and gravels, an undrained ring-shear test was carried out simulating the undrained loading process that takes place in the pre-existing slip surface. We have observed typical evolution of shear strength that found in the literature. This paper presents the research background and expected results from the ring-shear apparatus. At high shear speed, a temporary liquefaction and grain-crushing occurred in the sliding zone may take an important role in the long-runout landslide motion. Strength in rheology can be also determined in post-failure dynamics using ring-shear apparatus and be utilized in debris flow mobility.

• Journal of the Korea Furniture Society
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• v.23 no.2
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• pp.222-228
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• 2012

Seonreung is the tomb of Seong-jong (A.D. 1457~1494), the 9th king of Joseon Dynasty (1392-1910) and his second queen Jeonghyeon-wanghu (1462~1530). We obtained dendrochronological dates of Jeongjagak (ceremonial hall) of Seonreung. It was known first built in 1495 and reconstructed in October 1706, We obtained tree-ring dates of 20 wood elements (beams, pillars, truss posts, cant strips, roof boards and roof loaders). Their outermost rings were dated from 1630 to 1705. The dates of bark rings in four elements were A.D. 1705 with completed latewoods, indicating that these woods were cut some time between the autumn of 1705 and spring of 1706. The results confirmed the reconstruction date Jeongjagak of Seonreung in 1706, suggesting that there was not so long period for wood drying or storage, i.e., less than 6 months. The dates of outermost rings prior to 1705 in other elements indicated that some outer rings of these elements were removed during wood processing. Tree-ring dating proved that the present Jeongjagak of Seonreung had been well preserved for more than 300 years.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.117-119
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• 1985

Let R be a commutative noetherian ring with 1.neq.0, denoting by .nu.(I) the cardinality of a minimal basis of the ideal I. Let A be a polynomial ring in n>0 variables with coefficients in R, and let M be a maximal ideal of A. Generally it is shown that .nu.(M $A_{M}$).leq..nu.(M).leq..nu.(M $A_{M}$)+1. It is well known that the lower bound is not always satisfied, and the most classical examples occur in nonfactional Dedekind domains. But in many cases, (e.g., A is a polynomial ring whose coefficient ring is a field) the lower bound is attained. In [2] and [3], the conditions when the lower bound is satisfied is investigated. Especially in [3], it is shown that .nu.(M)=.nu.(M $A_{M}$) if M.cap.R=p is a maximal ideal or $A_{M}$ (equivalently $R_{p}$) is not regular or n>1. Hence the problem of determining whether .nu.(M)=.nu.(M $A_{M}$) can be studied when p is not maximal, $A_{M}$ is regular and n=1. The purpose of this note is to provide some conditions in which the lower bound is satisfied, when n=1 and R is a regular local ring (hence $A_{M}$ is regular)./ is regular).

• Journal of the Korean Society for Advanced Composite Structures
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• v.4 no.3
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• pp.38-44
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• 2013

Glass fiber reinforced plastic (GRP) pipes buried underground are attractive for use in harsh environments, such as for the collection and transmission of liquids which are abrasive and/or corrosive. In this paper, we present the result of investigation pertaining to the structural behavior of GRP flexible pipes buried underground. In the investigation of structural behavior such as a ring deflection, experimental and analytical studies are conducted. In addition, vertical ring deflection is measured by the field test and finite element analysis (FEA) is also conducted to simulate behavior of GRP pipe buried underground. Based on the results from the finite element analyses considering soil-pipe interaction the vertical ring deflection behavior of buried GRP pipe is predicted. In addition, analytical and experimental results are compared and discussed.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.157-167
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• 2011

For a ring endomorphism of a ring R, Krempa called $\alpha$ rigid endomorphism if $a{\alpha}(a)$ = 0 implies a = 0 for a $\in$ R, and Hong et al. called R an $\alpha$-rigid ring if there exists a rigid endomorphism $\alpha$. Due to Rege and Chhawchharia, a ring R is called Armendariz if whenever the product of any two polynomials in R[x] over R is zero, then so is the product of any pair of coefficients from the two polynomials. The Armendariz property of polynomials was extended to one of skew polynomials (i.e., $\alpha$-Armendariz rings and $\alpha$-skew Armendariz rings) by Hong et al. In this paper, we study the relationship between $\alpha$-rigid rings and extended Armendariz rings, and so we get various conditions on the rings which are equivalent to the condition of being an $\alpha$-rigid ring. Several known results relating to extended Armendariz rings can be obtained as corollaries of our results.

• Proceedings of the KOSOMBE Conference
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• v.1995 no.05
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• pp.173-178
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• 1995

This paper relates the occidental constitutional theory to the oriental one, concluding their origins to be similar, and demonstrates a new method of constitutional diagnosis by O-Ring Measurement System Of Muscular Meridians and Laser Constitutional Diagnosis. It establishes Laser Constitutional Diagnosis(L.C.D) using laser beams according to the principles of acupuncture and Sa-Sang constitutional physiology under the effect of spatial morphological energy of geometric isomers. Finally, hypothetical theory of L.C.D. was experimented by the O-Ring Measurement Systems of Muscular Meridians(O-R MSMM). O-R MSMM has been specially devised to improve the manual O-Ring Test prevailing to distinguish energetic response by muscle tonicity. Statistically, it has been proved that the constitutional diagnosis with O-R MSMM was highly effective and objective in the clinical experiences.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.491-498
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• 1995

This paper is concerned with an asymptotic behavior of ideals relative to injective modules ove the commutative Noetherian ring A : under what conditions on A can we show that $$\bar{At^*}(a,E)=At^*(a,E)$?

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.295-301
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• 1996

In this paper we will define correct module and strongly correct module. We can have some basic results about those modules. And we will show that M is a graded correct R-module if and only if $M_e$ is a correct $R_e$-module.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.755-762
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• 2006

For a commutative ring R and an injective cogenerator E in the category of R-modules, we characterize von Neumann regular rings and semisimple artinian rings in terms of the properties of dual modules with respect to E.