• Korean Journal of Acupuncture
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• v.18 no.1
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• pp.81-94
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• 2001

We could summerize the concept of the right and left mentioned in Nai-Gyung and some literature of oriental medicine as follow At first the right and left is a directional right and left which implys left-liver-right-lung(左肝右肺), left-yang-right-eum(左陽右陰), secondly it is also the road of eumyang which implys man-left-woman-right(男左女右), left-blood-right-ki(左血右氣), left-sinsu-right-myungmon(左腎水右命門), and left-right of pulse. left-liver-right-lung(左肝右肺), left-yang-right-eum(左陽右陰) and man-left-woman-right(男左女右) are expressions of the movement of yang which is a core of chang, at the same time, left-blood-right-ki(左血右氣), left-sinsu-right-myungmon(左腎水右命門), and left-right of pulse are expressions of the eum in response to the movement of yang. (go up and down of water and fire) Finally, both a directional right and left and a road of eumyang mean a road of going up and down of eumyang so, this is very important index in circulation and keeping ballance of eumyang (ki-Hyul:氣血) in the human body therefore, we can treat a disease with acupuncture in the use of this charater, for example when a disease occurs in the left side, we can treat it with acupuncture in the right side, the same applys to right.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1001-1015
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• 2023

We investigate the relationships between right (resp. left) interior systems and right (resp. left) interior operators on complete generalized residuated lattices. We show that the set induced by a right (resp. left) interior operator is right (resp. left) join complete.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.397-406
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• 2013

A ring R is called a left (right) SF-ring if simple left (right) R-modules are flat. It is still unknown whether a left (right) SF-ring is von Neumann regular. In this paper, we give some conditions for a left (right) SF-ring to be (a) von Neumann regular; (b) strongly regular; (c) division ring. It is proved that: (1) a right SF-ring R is regular if maximal essential right (left) ideals of R are weakly left (right) ideals of R (this result gives an affirmative answer to the question raised by Zhang in 1994); (2) a left SF-ring R is strongly regular if every non-zero left (right) ideal of R contains a non-zero left (right) ideal of R which is a W-ideal; (3) if R is a left SF-ring such that $l(x)(r(x))$ is an essential left (right) ideal for every right (left) zero divisor x of R, then R is a division ring.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.199-216
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• 2017

In the paper [Y. B. Jun, B. Davvaz and A. Khan, Filters of ordered semigroups based on the fuzzy points, JIFS 24 (2013) 619-630]. Jun et al. discussed the notion of (${\in},{\in}{\vee}q_k$)-fuzzy left (resp., right) filters as a generalization of the notion of (${\in},{\in}{\vee}q$)-fuzzy left (resp., right) filters of ordered semigroups. In this article, we try to obtain a more general form that (${\in},{\in}{\vee}q_k$)-fuzzy left (resp., right) filters in ordered semigroups. The notion of (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filters is discussed, and several properties are investigated. Characterizations of an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filter are established. A condition for an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filter to be a fuzzy left (resp., right) filter is provided. The important achievement of the study with an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (right) filter is that the notion of an (${\in},{\in}{\vee}q_k$)-fuzzy left ( right) filter and hence an (${\in},{\in}{\vee}q$)-fuzzy left (resp. right) filter are special cases of an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp. right) filter, and thus several results in published papers are becoming corollaries of our results obtained in this paper.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1321-1334
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• 2023

An idempotent e of a ring R is called right (resp., left) semicentral if er = ere (resp., re = ere) for any r ∈ R, and an idempotent e of R∖{0, 1} will be called right (resp., left) quasicentral provided that for any r ∈ R, there exists an idempotent f = f(e, r) ∈ R∖{0, 1} such that er = erf (resp., re = fre). We show the whole shapes of idempotents and right (left) semicentral idempotents of upper triangular matrix rings and polynomial rings. We next prove that every nontrivial idempotent of the n by n full matrix ring over a principal ideal domain is right and left quasicentral and, applying this result, we can find many right (left) quasicentral idempotents but not right (left) semicentral.

• Journal of the Ergonomics Society of Korea
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• v.18 no.2
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• pp.11-24
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• 1999

The purpose of this study was to obtain the basic data for sound wear design. The objects' of this study were 331 women's university students. The eight items were the shoulder length, shoulder slope, height, weight, chest girth, neck girth, back length, and back shoulder width. The shoulder length and slopes were measured, compared with the right, the left, and other items. The results were as follows; The difference between the right and left shoulder length did not nearly appear. The mean of the right shoulder slopes was $21.3^{\circ}$, and that of the left was $21.9^{\circ}$. According to increase of the age, the right and left shoulder slope tends to be higher. The maximum distribution was $20.7^{\circ}$. According to increase of the age, the maximum distribution tends to be higher. The left compared with the right shoulder length, the right shoulder length of 90.3% objects' was longer than that of the left. The right and left shoulder length of 4.2% objects' were same. The left shoulder length of 5.4% objects' was longer than that of the right. The left compared with the right shoulder slopes, the right shoulder slopes of 12.7% objects' were higher than those of the left. The both size of 20.5% objects' were equal. The left slopes of 66.8% objects' was higher than those of the right.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.263-267
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• 2008

Kaplansky introduced the Baer rings as rings in which every left (or right) annihilator of each subset is generated by an idempotent. On the other hand, Hattori introduced the left (resp. right) P.P. rings as rings in which every principal left (resp. right) ideal is projective. The purpose of this paper is to introduce the near-rings with Baer like condition and near-rings with P.P. like condition which are somewhat different from ring case, and to extend the results of Arendariz and Jondrup.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.315-321
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• 1996

Recently, N. Kehayopulu [4] introduced the concepts of weakly prime ideals of ordered semigroups. In this paper, we define the concepts of left(right) weakly prime and left(right) semiregular. Also we investigate the properties of them.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.607-623
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• 2013

Operational properties of cubic sets are first investigated. The notion of cubic subsemigroups and cubic left (resp. right) ideals are introduced, and several properties are investigated. Relations between cubic subsemigroups and cubic left (resp. right) ideals are discussed. Characterizations of cubic left (resp. right) ideals are considered, and how the images or inverse images of cubic subsemigroups and cubic left (resp. right) ideals become cubic subsemigroups and cubic left (resp. right) ideals, respectively, are studied.

• The korean journal of orthodontics
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• v.23 no.1 s.40
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• pp.1-15
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• 1993

This study was undertaken to investigate the midline having the least difference between the right and left structures among the lines that had been used in the study of the craniomaxillofacial asymmetry. The sample of this study consisted of twenty six Korean girls(average 18.9 years old) having normal facial appearance and occlusion. On the frontal cephalometric films of the sample, we divided the whole craniomaxillofacial area into four portions, i.e., cranial, upper facial, lower facial, and dental portion. So, we have found the midlines having the least difference in the whole craniomaxillofacial area itself, and in the each divided four portions, furtherly in the other portions from aimed portion. The findings were as follow: 1. In the whole craniomaxillofacial area, the connecting line between crista galli and anterior nasal spine and the perpendicular bisecting line between right and left foramen rotundums were suitable for the midline. 2. In the cranial portion, established all six lines were suitable for midlines. In the other portions, the perpendicular bisection line between both condylion, the line passing the contact point between right and left mandibular central insisiors among the perpendicular lines between right and left mandibular central incisial tips were suitable midlines fer evaluating the asymmetry of cranial portion. 3. In the upper facial portion, the perpendicular bisecting line between right and left zygions was the most suitable midline. In the other portions, the line between the crista galli and the most superior point of the odontoid process, the perpendicular bisecting line between right and left gonions, the perpendicular bisecting line between right and left condylions, and perpendicular bisecting line between right and left foramens rotundum were suitable midlines for evaluating the asymmetry of the upper facial portion 4. In the dental portion, the perpendicular bisecting lines between right and left buccal cusps of both maxillary first molars and between right and left mandibular first molars were suitable midlines. In the other portions, the perpendicular bisecting line between right and left landmarks crossing the lesser wing of the sphenoid bone and orbit, the perpendicular bisecting line between right and left mental foramens, and the connecting line between crista galli and prosthion were suitable midlines for evaluating the asymmetry of dental portion. 5. In the lower facial portion, the perpendicular bisecting lines between right and left condylions and between right and left gonions were suitable midlines. In the other portions, the line between the crista galli and anterior nasal spine, the perpendicular bisecting line between right and left foramen rotundums, and the perpendicular bisecting lines between right and left buccal cusps of both mandibular first molars and between right and left maxillary first molars were suitable midlines for evaluating the asymmetry of the lower facial portion.