• Title/Summary/Keyword: $R_m$

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NOTES ON THE REGULAR MODULES

  • Mohajer, Keivan;Yassemi, Siamak
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.693-699
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    • 1999
  • It is a well-known result that a commutative ring R is von Neumann regular if and only if for any maximal ideal m of R the R-module R/m is flat. In this note we bring a generalization of this result for modules.

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A FINITE ADDITIVE SET OF IDEMPOTENTS IN RINGS

  • Han, Juncheol;Park, Sangwon
    • Korean Journal of Mathematics
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    • v.21 no.4
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    • pp.463-471
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    • 2013
  • Let R be a ring with identity 1, $I(R){\neq}\{0\}$ be the set of all nonunit idempotents in R, and M(R) be the set of all primitive idempotents and 0 of R. We say that I(R) is additive if for all e, $f{\in}I(R)$ ($e{\neq}f$), $e+f{\in}I(R)$. In this paper, the following are shown: (1) I(R) is a finite additive set if and only if $M(R){\backslash}\{0\}$ is a complete set of primitive central idempotents, char(R) = 2 and every nonzero idempotent of R can be expressed as a sum of orthogonal primitive idempotents of R; (2) for a regular ring R such that I(R) is a finite additive set, if the multiplicative group of all units of R is abelian (resp. cyclic), then R is a commutative ring (resp. R is a finite direct product of finite field).

Flow Resistance and Modeling Rule of Fishing Nets 4. Flow Resistance of Trawl Nets (그물어구의 유수저항과 모형수칙 4. 트롤그물의 유수저항)

  • KIM Dae-An
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.30 no.5
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    • pp.691-699
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    • 1997
  • In order to find out the properties in flow resistance of trawlR=1.5R=1.5\;S\;v^{1.8}\;S\;v^{1.8} nets and the exact expression for the resistance R (kg) under the water flow of velocity v(m/sec), the experimental data on R obtained by other, investigators were pigeonholed into the form of $R=kSv^2$, where $k(kg{\cdot}sec^2/m^4)$ was the resistance coefficient and $S(m^2)$ the wall area of nets, and then k was analyzed by the resistance formular obtained in the previous paper. The analyzation produced the coefficient k expressed as $$k=4.5(\frac{S_n}{S_m})^{1.2}v^{-0.2}$$ in case of bottom trawl nets and as $$k=5.1\lambda^{-0.1}(\frac{S_n}{S_m})^{1.2}v^{-0.2}$$ in midwater trawl nets, where $S_m(m^2)$ was the cross-sectional area of net mouths, $S_n(m^2)$ the area of nets projected to the plane perpendicular to the water flow and $\lambda$ the representitive size of nettings given by ${\pi}d^2/2/sin2\varphi$ (d : twine diameter, 2l: mesh size, $2\varphi$ : angle between two adjacent bars). The value of $S_n/S_m$ could be calculated from the cone-shaped bag nets equal in S with the trawl nets. In the ordinary trawl nets generalized in the method of design, however, the flow resistance R (kg) could be expressed as $$R=1.5\;S\;v^{1.8}$$ in bottom trawl nets and $$R=0.7\;S\;v^{1.8}$$ in midwater trawl nets.

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Marginal fidelity of zirconia core using MAD/MAM system (MAD/MAM을 이용한 치과용 지르코니아 코어의 변연 적합도)

  • Kang, Dong-Rim;Shim, June-Sung;Moon, Hong-Suk;Lee, Keun-Woo
    • The Journal of Korean Academy of Prosthodontics
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    • v.48 no.1
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    • pp.1-7
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    • 2010
  • Purpose: The purpose of this study was to evaluate the fit of zirconia core using MAD/MAM system comparing to that of conventional metal-ceramic and CAD/CAM system. Materials and methods: Duplicating the prepared resin tooth, 50 improved stone dies were fabricated. These dies are classified as a group of 5 to create the core. The groups were composed of metal-ceramic, $Cercon^{(R)}$, $Ceramill^{(R)}$, $Rainbow^{TM}$, and $Zirkonzhan^{(R)}$. Each core was cemented to stone die, and then, absolute marginal discrepancy was measured with microscope at a magnification of ${\times}50$. Statistical analysis was done with one-way ANOVA test and Tukey's HSD test. Results: The mean absolute marginal discrepancy for metal-ceramic was $51.97{\pm}23.38{\mu}m$, for $Cercon^{(R)}$ was $62.16{\pm}25.88{\mu}m$, for $Ceramill^{(R)}$ was $67.64{\pm}40.38{\mu}m$, for $Rainbow^{TM}$ was $125.07{\pm}42.19{\mu}m$, and for $Zirkonzhan^{(R)}$ was $105{\pm}44.61{\mu}m$. Conclusion: 1. Fit of margin was identified as in the order of metal-ceramic, $Cercon^{(R)}$, $Ceramill^{(R)}$, $Zirkonzhan^{(R)}$, and $Rainbow^{TM}$. 2. Absolute marginal discrepancy of the zirconia core that designed by MAD/MAM system had significant differences in order of $Ceramill^{(R)}$, $Zirkonzhan^{(R)}$, and $Rainbow^{TM}$. 3. The mean absolute marginal discrepancy between $Cercon^{(R)}$ and $Ceramill^{(R)}$ did not show significant differences.

Stability of Cefditoren in Three Oral Liquid Preparations (경구용 시럽제 중 세프디토렌의 안정성에 관한 연구)

  • Kim, Hye-Kyung;Gwak, Hye-Sun
    • Korean Journal of Clinical Pharmacy
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    • v.16 no.1
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    • pp.28-33
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    • 2006
  • The stability of cefditoren in three kinds of oral liquid preparations at 4 and $25^{\circ}C$ was studied for 90 days. Two tablets of 100 mg cefditoren pivoxil were mixed with 200 mL of each oral liquid syrup, which is Pebron syrup (oxolamine citrate 10 mg/mL), $Mucopect^{(R)}$ syrup (ambroxol hydrochloride 3 mg/mL) or $Tyrenol^{(R)}$ suspension (acetaminophen encapsulated 32 mg/mL). Three samples of each formulation were refrigerated $(4^{\circ}C)$ and three were stored at room temperature $(25^{\circ}C)$. At predetermined time, samples were assayed by stability-indicating HPLC method. The chromatographic analysis after deliberate degradation showed no evidence of any breakdown product likely to interfere with the chromatographic peak of the parent substance. The relation between cefditoren pivoxil concentration and peak area was linear from 10 to $150{\mu}g/mL\;(r^2=0.9998)$. The analysis method was precise, with coefficients of variation no greater than 3.6%. Cefditoren was stable in $Mucopect^{(R)}$ syrup up to 4 weeks regardless of the temperature; in $Tyrenol^{(R)}$ suspension and Pebron syrup, it was stable for at least 28 and 45 days, and 7 and 45 days at 25 and $4^{\circ}C$, respectively. The percentages of initial cefditoren concentration remaining after 90 days were $51.5{\pm}1.8\;and\;80.9{\pm}5.6%,\;61.7{\pm}7.8\;and\;70.2{\pm}7.3%,\;and\;39.9{\pm}3.2\;and\;81.4{\pm}5.5%$ in $Mucopect^{(R)}$ syrup, $Tyrenol^{(R)}$ suspension and $Pebron^{(R)}$ syrup at 25 and $4^{\circ}C$, respectively. The pH variations of all test solutions were minimal, which was within 0.5. The results indicated that the stability of cefditoren was significantly affected by liquid solutions mixed with cefditoren, and storage tempertature.

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RESOLUTIONS AND DIMENSIONS OF RELATIVE INJECTIVE MODULES AND RELATIVE FLAT MODULES

  • Zeng, Yuedi;Chen, Jianlong
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.11-24
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    • 2013
  • Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be ($m$, $n$)-injective if $Ext^1$(P, M) = 0 for any ($m$, $n$)-presented right R-module P; M is said to be ($m$, $n$)-flat if $Tor_1$(N, P) = 0 for any ($m$, $n$)-presented left R-module P. In terms of some derived functors, relative injective or relative flat resolutions and dimensions are investigated. As applications, some new characterizations of von Neumann regular rings and p.p. rings are given.

INJECTIVE REPRESENTATIONS OF QUIVERS

  • Park, Sang-Won;Shin, De-Ra
    • Communications of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.37-43
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    • 2006
  • We prove that $M_1\longrightarrow^f\;M_2$ is an injective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ if and only if $M_1\;and\;M_2$ are injective left R-modules, $M_1\longrightarrow^f\;M_2$ is isomorphic to a direct sum of representation of the types $E_l{\rightarrow}0$ and $M_1\longrightarrow^{id}\;M_2$ where $E_l\;and\;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1\longrightarrow^{f_1}\;M_2\; \longrightarrow^{f_2}\;\cdots\;\longrightarrow^{f_{n-1}}\;M_n$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\cdots}{\rightarrow}{\bullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.

ON WEAKLY (m, n)-PRIME IDEALS OF COMMUTATIVE RINGS

  • Hani A. Khashan;Ece Yetkin Celikel
    • Bulletin of the Korean Mathematical Society
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    • v.61 no.3
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    • pp.717-734
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    • 2024
  • Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of weakly (m, n)-prime ideals generalizing (m, n)-prime and weakly (m, n)-closed ideals. A proper ideal I of R is called weakly (m, n)-prime if for a, b ∈ R, 0 ≠ amb ∈ I implies either an ∈ I or b ∈ I. We justify several properties and characterizations of weakly (m, n)-prime ideals with many supporting examples. Furthermore, we investigate weakly (m, n)-prime ideals under various contexts of constructions such as direct products, localizations and homomorphic images. Finally, we discuss the behaviour of this class of ideals in idealization and amalgamated rings.