• 대한수학회지
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• 제45권2호
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• pp.425-433
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• 2008

Let R be a ring with identity $1_R$ and let U(R) denote the group of all units of R. A ring R is called locally finite if every finite subset in it generates a finite semi group multiplicatively. In this paper, some results are obtained as follows: (1) for any semilocal (hence semiperfect) ring R, U(R) is a finite (resp. locally finite) group if and only if R is a finite (resp. locally finite) ring; U(R) is a locally finite group if and only if U$(M_n(R))$ is a locally finite group where $M_n(R)$ is the full matrix ring of $n{\times}n$ matrices over R for any positive integer n; in addition, if $2=1_R+1_R$ is a unit in R, then U(R) is an abelian group if and only if R is a commutative ring; (2) for any semiperfect ring R, if E(R), the set of all idempotents in R, is commuting, then $R/J\cong\oplus_{i=1}^mD_i$ where each $D_i$ is a division ring for some positive integer m and |E(R)|=$2^m$; in addition, if 2=$1_R+1_R$ is a unit in R, then every idempotent is central.

• 대한수학회지
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• 제54권1호
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• pp.177-191
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• 2017

In this note we consider the right unit-duo ring property on the powers of elements, and introduce the concept of weakly right unit-duo ring. We investigate first the properties of weakly right unit-duo rings which are useful to the study of related studies. We observe next various kinds of relations and examples of weakly right unit-duo rings which do roles in ring theory.

• 대한수학회논문집
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• 제35권1호
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• pp.117-124
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• 2020

In 2013, Diesl defined a nil clean ring as a ring of which all elements can be expressed as the sum of an idempotent and a nilpotent. Furthermore, in 2017, Y. Zhou, S. Sahinkaya, G. Tang studied nil clean group rings, finding both necessary condition and sufficient condition for a group ring to be a nil clean ring. We have proposed a necessary and sufficient condition for a group ring to be a uniquely nil clean ring. Additionally, we provided theorems for general nil clean group rings, and some examples of trivial-center groups of which group ring is not nil clean over any strongly nil clean rings.

• East Asian mathematical journal
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• 제25권4호
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• pp.433-440
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• 2009

Let R be a ring with unity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will consider some group actions on X by G, the left (resp. right) regular action and the conjugate action. In this paper, by investigating these group actions we can have some results as follows: First, if E(R), the set of all nonzero nonunit idempotents of a unit-regular ring R, is commuting, then $o_{\ell}(x)\;=\;o_r(x)$, $o_c(x)\;=\;\{x\}$ for all $x\;{\in}\;X$ where $o_{\ell}(x)$ (resp. $o_r(x)$, $o_c(x)$) is the orbit of x under the left regular (resp. right regular, conjugate) action on X by G and R is abelian regular. Secondly, if R is a unit-regular ring with unity 1 such that G is a cyclic group and $2\;=\;1\;+\;1\;{\in}\;G$, then G is a finite group. Finally, if R is an abelian regular ring such that G is an abelian group, then R is a commutative ring.

• 대한수학회논문집
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• 제33권4호
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• pp.1075-1082
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• 2018

Let R be a commutative ring, G be an Abelian group, and let RG be the group ring. We say that RG is a U-group ring if a is a unit in RG if and only if ${\epsilon}(a)$ is a unit in R. We show that RG is a U-group ring if and only if G is a p-group and $p{\in}J(R)$. We give some properties of U-group rings and investigate some properties of well known rings, such as Hermite rings and rings with stable range, in the presence of U-group rings.

• 대한수학회보
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• 제60권1호
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• pp.83-91
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• 2023

A ring R is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal I of a UN ring R. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring R, a matrix ring M_n(R) is UN if and only if R is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group G and a field K for the group algebra KG to be UN. Then we extend the results obtained for KG to the group ring RG over a ring R (which may not necessarily be a field).

• 대한수학회지
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• 제58권1호
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• pp.149-171
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• 2021

Let Cl(A) denote the class group of an arbitrary integral domain A introduced by Bouvier in 1982. Then Cl(A) is the ideal class (resp., divisor class) group of A if A is a Dedekind or a Prüfer (resp., Krull) domain. Let G be an abelian group. In this paper, we show that there is a ring of Krull type D such that Cl(D) = G but D is not a Krull domain. We then use this ring to construct a Prüfer ring of Krull type E such that Cl(E) = G but E is not a Dedekind domain. This is a generalization of Claborn's result that every abelian group is the ideal class group of a Dedekind domain.

• Journal of Acupuncture Research
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• 제19권3호
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• pp.77-87
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• 2002

Like acupuncture, magnetic therapy has been known to yield effectiveness when it is applied to relieve from fatigue, musculoskelectal diseases, sore sites, rheumatic arthritis and chronic pain syndromes. However, combined application of acupuncture and magnet has not yet been studied. This study is designed to investigate effectiveness of acupuncture therapy when in the magnetic field for the pain relief. Magnetic field was made by magnetic ring ($7{\psi}{\times}2.3{\psi}{\times}1.5mm$). Twenty-one male swimmers with latent muscular pain at the GB21 area in the university course of physical education in Daegu were chosen and divided into three groups; 1) acupuncture treatment group (n=7), 2) acupuncture treatment with iron ring group (n=7), 3) acupuncture treatment with magnetic ring group (n=7). Manual Acupuncture was given to the GB21 point for 20 minutes. The degree of pressure pain threshold (PPT, $kg/cm^2$) in GB21 was measured with algometer. Before acupuncture treatment, the PPT values were $6.08{\pm}1.69$, $6.39{\pm}1.72$ and $5.59{\pm}1.11$ in acupuncture treatment group, acupuncture treatment with iron ring group, acupuncture treatment with magnetic ring group, respectively. After acupuncture treatment, the PPT values were $6.48{\pm}2.33$, $6.31{\pm}1.31$ and $6.59{\pm}1.80$, respectively. Pressure threshold was significantly increased in the acupuncture treatment with magnetic ring group compared to the other groups. Based on these results, acupuncture treatment with magnetic ring produced better effects on pain threshold, and these effects can be considered to be associated with the currents or voltages induced by the acupuncture needle and magnetic ring at present.

• 정보처리학회논문지A
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• 제14A권6호
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• pp.333-340
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• 2007

일반적인 멀티에이전트 시스템에서 에이전트들 간의 통신 기능을 지원하기 위한 다양한 모델들이 제안되어 왔으며, 특히, 그룹 통신 기능을 지원하기 위한 다양한 기법들이 제시되어 있다. 그러나, 이동 에이전트 환경에서는 에이전트의 이주로 인해 발생하는 토폴로지의 변화를 고려한 새로운 그룹 통신 기법을 필요로 하며, 더불어 이러한 그룹 통신 기능의 안전성을 보장하는 기법이 필요하게 된다. 본 논문에서는 계층적 오버레이 링을 이용한 이동 에이전트들 간의 안전한 그룹 통신 기법을 제안하며, 이 기법은 이동 에이전트의 이주에 따른 토폴로지의 변화에 유연하게 대응하기 위해 링 채널을 이용한다. 여기서 링 채널은 이동 에이전트들 간의 링 토폴로지를 구성하기 위한 객체로서 이동 에이전트 플랫폼에 의해서만 관리되며, 이에 따라 이동 에이전트들은 링 채널을 직접 관리할 필요가 없게 되고, 이주에 의해 발생하는 링 토폴로지 변화에 대한 고려 없이 그룹 통신을 진행할 수 있게 된다.

• 분석과학
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• 제24권3호
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• pp.173-182
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• 2011

약물(Prostanozol)을 복용한 여성을 대상으로 한 뇨시료 중에 함유된 Prostanozol 및 그 대사체들을 검출하기 위해 LC/ESI/MS와 GC/TOF-MS를 이용하여 효과적으로 분리 및 검출하였고, LC/ESI/MS의 질량스펙트럼으로부터는 각각의 분자량을 추정하였으며 GC/TOF-MS로는 이들을 확인하였다. M1은 Prostanozol의 17번 탄소가 케톤기로 치환된 17-keto-Prostanozol, M2는 M1에서 pyrazole nucleus 와 Aring에 한 개의 히드록시기가 치환된 hydroxy-17-keto-Prostanozol, M3는 B-ring 또는 C-ring에 한 개의 히드록시기가 치환된 hydroxy-17-keto-Prostanozol, M4는 한 개의 히드록시기가 D-ring에 치환된 hydroxy-17-keto-Prostsnozol로 확인되었으며 M5는 17번 탄소 위치에 히드록시기를 갖고 B-ring 또는 C-ring에서 하나의 히드록시기가 치환된 hydroxy-17-hydroxy-Prostanozol로 추정되며 M6은 17번 탄소 위치에 케톤기를 갖고 pyrazole nucleus 혹은 A-ring에 하나의 히드록시기를 또한 B-ring 또는 C-ring에 또 하나의 히드록시기가 치환된 dihydroxy-17-keto-Prostanozol, M7은 M6와 같이 17번 탄소에 케톤기를 갖으며 pyrazole nucleus 혹은 A-ring에 하나의 히드록시기를, 또한 D-ring에 또 하나의 히드록시기를 가진 dihydroxy-17-keto-Prostanozol로 확인되었다. 마지막으로 M8은 pyrazole nucleus 혹은 A-ring에 하나의 히드록시기를 갖고 그 외의 ring에 또 다른 히드록시기가 치환된 dihydroxy-17-hydroxy-Prostanozol임을 확인할 수 있었다. 이중 M5, M7, 그리고 M8은 지금까지 밝혀지지 않았던 새로운 대사체였다. 체내에서의 포합반응 여부를 확인한 결과 Prostanozol과 8종의 모든 대사체가 글루쿠론산 포합체를 형성하였고, 8종의 대사체 중 일부는 포합체를 형성하지 않고도 배출되며 특히 M6과 M7은 황산 포합체로도 배설되는 것을 확인할 수 있었다.