• Title/Summary/Keyword: Division ring

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A NOTE ON ARTINIAN LOCAL RINGS

  • Hu, Kui;Kim, Hwankoo;Zhou, Dechuan
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.5
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    • pp.1317-1325
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    • 2022
  • In this note, we prove that an Artinian local ring is G-semisimple (resp., SG-semisimple, 2-SG-semisimple) if and only if its maximal ideal is G-projective (resp., SG-projective, 2-SG-projective). As a corollary, we obtain the global statement of the above. We also give some examples of local G-semisimple rings whose maximal ideals are n-generated for some positive integer n.

ON WEAK ARMENDARIZ RINGS

  • Jeon, Young-Cheol;Kim, Hong-Kee;Lee, Yang;Yoon, Jung-Sook
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.1
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    • pp.135-146
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    • 2009
  • In the present note we study the properties of weak Armendariz rings, and the connections among weak Armendariz rings, Armendariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime right Goldie ring R is weak Armendariz if and only if R is Armendariz if and only if R is reduced if and only if R is IFP if and only if Q is a finite direct product of division rings, obtaining a simpler proof of Lee and Wong's result. In the process we construct a semiprime ring extension that is infinite dimensional, from given any semi prime ring. We next find more examples of weak Armendariz rings.

A NOTE ON LOCAL COMMUTATORS IN DIVISION RINGS WITH INVOLUTION

  • Bien, Mai Hoang
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.659-666
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    • 2019
  • In this paper, we consider a conjecture of I. N. Herstein for local commutators of symmetric elements and unitary elements of division rings. For example, we show that if D is a finite dimensional division ring with involution ${\star}$ and if $a{\in}D^*=D{\setminus}\{0\}$ such that local commutators $axa^{-1}x^{-1}$ at a are radical over the center F of D for every $x{\in}D^*$ with $x^{\star}=x$, then either $a{\in}F$ or ${\dim}_F\;D=4$.

FUZZY IDEALS AND FUZZY SUBRINGS UNDER TRIANGULAR NORMS

  • Chon, Inheung
    • Korean Journal of Mathematics
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    • v.10 no.2
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    • pp.149-155
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    • 2002
  • We develop some basic properties of $t$-fuzzy ideals in a monoid or a group and find the sufficient conditions for a fuzzy set in a division ring to be a $t$-fuzzy subring and the necessary and sufficient conditions for a fuzzy set in a division ring to be a $t$-fuzzy ideal.

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A Study on Design of Band Pass Filter using Ring Resonators (링 공진기를 사용한 대역통과 필터의 설계에 관한 연구)

  • Kim, Dong-Il;Kim, Bo-Young;Rui, Li
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.15 no.6
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    • pp.533-539
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    • 2004
  • In this work, in order to realize a band pass filter with wide-band characteristics for mobile communications, 2 GHz band pass filter was designed using ring resonator with stub. The three stage wide-band BPF was designed and fabricated. For broadband design, the ring circumference was divided by 4 sections with 1/8 wavelength and 2 sections with 1/4 wavelength which have different line impedances. The characteristics of the proposed BPF were highly improved by using three stage ring resonator. The characteristic impedance values of each sections were obtained by Powell's least square algorithm where differentiations are not needed. The measured results showed a good agreement with the theoretical results as well as ADS simulation.

Leaf Rot and Leaf Ring Spot Caused by Rhizoctonia solani in Chinese Cabbage

  • Shim, Chang-Ki;Kim, Min-Jeong;Kim, Yong-Ki;Jee, Hyeong-Jin;Hong, Sung-Jun;Park, Jong-Ho;Han, Eun-Jung;Yun, Jong-Chul
    • Research in Plant Disease
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    • v.19 no.4
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    • pp.300-307
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    • 2013
  • This study was conducted to determine the occurrence of leaf rot and leaf ring spot, caused by Rhizoctonia solani in Chinese cabbage under seedling nursery and cultivation greenhouses. Symptoms of leaf rot and leaf ring spot were found in three Chinese cabbage cultivars, Brassica campestris subsp. pekinensis, 'Ryeokgwang', 'Daetong', and 'CR mat'. In Hwacheon, the disease incidence was 73.8% in the seedling stage of the Chinese cabbage. In Icheon, the symptoms were observed on the upper leaves of the Chinese cabbage cultivar, 'Norangmini' with 20.5% of disease incidence. The symptoms appeared as primary lesions consisting of small, circular necrotic ring spots with gray color, 1.4-3.0 mm in diameter, accompanied by secondary rot lesions with large irregular borders of leaves. The color of mycelial mat of 20 isolates was dark brown and light brown. The average hyphal diameter of all the isolates was within 5.01-11.12 ${\mu}m$. Among the 20 strains isolated from Chinese cabbage, 16 isolates and four isolates anastomosed with the AG-1 (IB) and AG-1 (IC), respectively. Twenty isolates tested were only virulent on foliage parts of Chinese cabbage leaves but were avirulent on stem parts of the plants. Based on the mycological characteristics and pathogenicity test on host plants, the fungus was identified as Rhizoctonia solani.

Ring-Opening Metathesis Polymerization and Hydrogenation of Ethyl-substituted Tetracyclododecene

  • Kwon, Oh-Joon;Vo, Huyen Thanh;Lee, Sul-Bee;Kim, Tae-Kyung;Kim, Hoon-Sik;Lee, Hyun-Joo
    • Bulletin of the Korean Chemical Society
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    • v.32 no.8
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    • pp.2737-2742
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    • 2011
  • Ring-opening metathesis polymerization (ROMP) of an ethyl-substituted tetracyclododecene (8-ethyltetracyclo[$4.4.0.1^{2,5}.1^{7,10}$] dodec-3-ene, Et-TCD) was carried out in the presence of a ternary catalyst system consisting of $WCl_6$, triisobutyl aluminium (iso$Bu_3Al$), and ethanol. The optimal molar ratio of Et-TCD/$WCl_3$/iso-$Bu_3Al$/ethanol was found as 500/1/3/2 at which the yield of ring-opened polymer was 100%. 1-Hexene was shown to be an effective molecular weight controlling agent for ROMP reaction of Et-TCD. The hydrogenation of the ring opened polymer (p-Et-TCD) was conducted successfully using Pd(5 wt %)/${\gamma}$-$Al_2O_3$ at $80^{\circ}C$ for 1 h. Chemical structures of p-Et-TCD and its hydrogenated product($H_2$-p-Et-TCD) were characterized using 2D NMR techniques ($^1H-^1H$ COSY and $^1H-^{13}C$ HSQC). The changes of physical properties such as thermal stability, glass transition temperature and light transmittance after the hydrogenation were also investigated using TGA, DSC, and UV.

A Study of Material and Production Technique of Scroll Painting Ring in Joseon (조선시대 족자 장황에 사용된 고리의 재료 및 제작기법 연구)

  • Jang, Yeonhee;Yun, Eunyoung;Kwon, Yoonmi;Kim, Sooyeon
    • Conservation Science in Museum
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    • v.16
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    • pp.56-81
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    • 2015
  • Ring in the scroll painting is one of the mounting elements which are fixed string and tassel to hang, these differ widely in shape and produce a variety of metals. Most traditional shapes of ring have been lost, because of remount, there are used Japanese style rings in present.Therefore, this study examines to shape, production technique and analyze component traditional style rings of 19 traditional scroll paintings in National Museum of Korea for restoration of original style. Ring has been recorded official names; Wonhwan(Ring), Gukhwadong(Chrysanthemum shaped ornaments), Baemok(Ring-shaped nail) in Uigwe. Result of an optical microscope (Leica, M205A), Wonhwan has two type of production technique; one is cutting and bending a metal rod and other is cast. Baemok is made to forging process after metal rod or plate by casting alloy. Baemok decoration is metal plate cutting shape, and then decorates it with pattern by using kicking line engraving, chasing and so on. Component analysis result from portable X-ray fluorescence found various metals, such as, brass, iron silver-cooper. Brass based on copper and zinc used rings of 17 scroll painting. Baemok of Yun Sidal portrait is used iron and plated with a tin-lead alloy. Yi Seogu portrait is silver-cooper alloy in whole ring.