• Journal of the Korean Mathematical Society
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• v.45 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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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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• v.25 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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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).

• Journal of the Korean Mathematical Society
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• v.58 no.1
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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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• v.19 no.3
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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.

• The KIPS Transactions:PartA
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• v.14A no.6
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• pp.333-340
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• 2007

In multi agent systems, various inter agent communication models have been proposed, and, especially, there are several group communication schemes proposed so far, where some schemes guarantees transparent communication among the agents. However, in mobile agent environments, we require new group communication schemes that consider topology changes caused by mobile agent migrations. Also, these group communication schemes should be secure in order for them to be practical. In this paper, we propose a secure group communication scheme using the hierarchical overlay ring structure of mobile agents. The proposed scheme uses the ring channel in order to cope adaptively with the change of ring topology. The ring channel has basic information for construction of the ring and is managed only by the mobile agent platforms. Therefore, each mobile agent need not directly handle the ring channel and it can perform group communication without any consideration on the change of the ring topology.

• Analytical Science and Technology
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• v.24 no.3
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• pp.173-182
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• 2011

This research examined prostanozol and its metabolites in urine of women who took the medicine (prostanozol). Prostanozol and its metabolites were successfully separated and detected by using LC/ESI/MS and GC/TOF-MS. Mass spectrum of LC/ESI/MS estimated molecular weight of Prostanozol and its metabolites and that of GC/TOF-MS verified them. For M1, carbon number 17 of Prostanozol substituted to a keto group and it is called 17-keto-Prostanozol. M2 turned out to be hydroxy-17-keto-Prostanozol. It came from substitution of one hydroxyl group of pyrazole nucleus and A-ring of M1. Substitution of one hydroxyl group of B-ring or C-ring became M3, hydroxy-17-keto-Prostanozol. M4 was found to be a hydroxy-17-keto-Prostsnozol transposed from one hydroxyl group to a D-ring. M5 has a hydroxyl group of carbon number 17. One hydroxyl group is substituted from B-ring or C-ring and it is assumed to be hydroxy-17-hydroxy-Prostanozol. M6 was turned out to be dihydroxy-17-keto-Prostanozol transposed from one hydroxyl group to pyrazole nucleus or A-ring and to B-ring or C-ring. Like M6, M7 has a keto group at carbon number 17 and was identified as dihydroxy-17-keto-Prostanozol. M7 has one hydroxyl group at pyrazole nucleus or A-ring and also at D-ring. At last M8 was found to be dihydroxy-17-hydroxy-Prostanozol. Pyrazole nucleus or A-ring has got one hydroxyl group and other rings were substituted to another hydroxyl group. From above, M5, M7 and M8 were verified as new metabolites that were not discovered yet. Prostanozol and all of the 8 metabolites formed glucuronic conjugates as a result of conjugation reaction test in human body. Some of 8 metabolites were excreted without forming conjugates. Particularly M6 and M7 were excreted as sulfate conjugates.