• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.645-652
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• 2002

In this note we investigate some results which concern the types of local rings. In particular it is shown that if the type of a quasi-unmixed local ring A is less than or equal to depth A ＋ 1, and $\hat{A}_p$ is Cohen-Macaulay for every prime $p\neq\hat{m}$, then A is Cohen-Macaulay. (This implies the previously known result: if A satisfies $(S_{n-1})}$, where n is the type of a .ins A, then A is Cohen-Macaulay.)

• Proceedings of the Microbiological Society of Korea Conference
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• 2000.10a
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• pp.39-45
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• 2000

It hab been proposed that CHS3-mediated chitin synthesis during the vegitative cell cycle is regulated by CHS4. To investigate direct protein-protein interaction between their coding products, we used yeast two hybrid system and found that a domain of Chs3p was responsible for interaction with Chs4p. This domain, termed MIRC3-4 (maximum interacting region of chs3p with chs4p), spans from 647 to 700 residues. It is well conserved among CHS3 homologs of various fungi such as Candida albicans, Emericella nidulans, Neurospora crassa, Magnaporthe grisea, Ustilago maydis, Glomus versiforme, Exophiala dermatitidis, Rhizopus microsporus. A series of mutaion in the MIRC3-4 resulted in no appearance of chitin ring at the early G 1 phase but did not affect chitin synthesis in the cell wall after cytokinesis. Absence of chitin ring could be caused either by delocalization of Chs3p to the septum or by improper interaction with Chs4p. To discriminate those two, not mutually exclusive, alternatives, mutants cells were immunostained with Chs3p-specific antibody. Some exhibited localization of chs3p to the septum, while others failed. These results indicate that simultaneous localization and activation Chs3p by Chs4p is required for chitin ring synthesis.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.223-234
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• 2003

This note contains the following results for a ring A : (1) A is simple Artinian if and only if A is a prime right YJ-injective, right and left V-ring with a maximal right annihilator ; (2) if A is a left quasi-duo ring with Jacobson radical J such that $_{A}$A/J is p-injective, then the ring A/J is strongly regular ; (3) A is von Neumann regular with non-zero socle if and only if A is a left p.p.ring containing a finitely generated p-injective maximal left ideal satisfying the following condition : if e is an idempotent in A, then eA is a minimal right ideal if and only if Ae is a minimal left ideal ; (4) If A is left non-singular, left YJ-injective such that each maximal left ideal of A is either injective or a two-sided ideal of A, then A is either left self-injective regular or strongly regular : (5) A is left continuous regular if and only if A is right p-injective such that for every cyclic left A-module M, $_{A}$M/Z(M) is projective. ((5) remains valid if 《continuous》 is replaced by 《self-injective》 and 《cyclic》 is replaced by 《finitely generated》. Finally, we have the following two equivalent properties for A to be von Neumann regula. : (a) A is left non-singular such that every finitely generated left ideal is the left annihilator of an element of A and every principal right ideal of A is the right annihilator of an element of A ; (b) Change 《left non-singular》 into 《right non-singular》in (a).(a).

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1617-1628
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• 2016

In this paper, we extend the results given in [3] to a nonchain ring $R_p={\mathbb{F}}_p+v{\mathbb{F}}_p+{\cdots}+v^{p-1}{\mathbb{F}}_p$, where $v^p=v$ and p is a prime. We determine the structure of the cyclic codes of arbitrary length over the ring $R_p$ and study the structure of their duals. We classify cyclic codes containing their duals over $R_p$ by giving necessary and sufficient conditions. Further, by taking advantage of the Gray map ${\pi}$ defined in [4], we give the parameters of the quantum codes of length pn over ${\mathbb{F}}_p$ which are obtained from cyclic codes over $R_p$. Finally, we illustrate the results by giving some examples.

• Korean Journal of Optics and Photonics
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• v.20 no.1
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• pp.41-47
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• 2009

We report the spectral characteristics of Multimode Interferometer (MMI)-coupled semicondoctor square ring resonators. The epitaxial layers of the proposed semiconductor ring resonator consists of $1.55{\mu}m$ GaInAsP-InP multiple quantum wells. The lasing characteristics were observed by varying the structure parameters of the MMI-coupled square ring resonators. It is concluded that the MMI-coupled scheme selects a single spectral lasing mode in the double square ring cavities.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.571-583
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• 2020

The Galois ring R of characteristic pⁿ having p^mn elements is a finite extension of the ring of integers modulo pⁿ, where p is a prime number and n, m are positive integers. In this paper, we develop the concepts of Jacobi sums over R and under the assumption that the generating additive character of R is trivial on maximal ideal of R, we obtain the basic relationship between Gauss sums and Jacobi sums, which allows us to determine the absolute value of the Jacobi sums.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.207-213
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• 2010

In this paper, we define the q-extension of the Hardy-Littlewood-type maximal operator related to q-Volkenborn integral. By the meaning of the extension of q-Volkenborn integral, we obtain the boundedness of the q-extension of the Hardy-Littlewood-type maximal operator in the p-adic integer ring.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.678-681
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• 2023

Let G be a cyclic group of prime power order p^k, and let I be the augmentation ideal of the integral group ring ℤ[G]. We define a derivation on ℤ/p^kℤ[G], and show that for 2 ≤ n ≤ p, an element α ∈ I is in Iⁿ if and only if the i-th derivative of the image of α in ℤ/p^kℤ[G] vanishes for 1 ≤ i ≤ (n - 1).

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.163-165
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• 1994

Modules which satisfy the converse of Schur's lemma have been studied by many authors. In [6], R. Ware proved that a projective module P over a semiprime ring R is irreducible if and only if En $d_{R}$(P) is a division ring. Also, Y. Hirano and J.K. Park proved that a torsionless module M over a semiprime ring R is irreducible if and only if En $d_{R}$(M) is a division ring. In case R is a commutative ring, we obtain the following: An R-module M is irreducible if and only if En $d_{R}$(M) is a division ring and M is a multiplication R-module. Throughout this paper, R is commutative ring with identity and all modules are unital left R-modules. Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for each submodule N of M, there exists and ideal I of R such that N=IM. Cyclic R-modules are multiplication modules. In particular, irreducible R-modules are multiplication modules.dules.

• Korean Journal of Environmental Agriculture
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• v.22 no.2
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• pp.118-123
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• 2003

This study was carried out to examine the heavy metal concentrations in soils under roadside trees and tree ring layers, and to investigate the relationship between heavy metal concentrations and tree ring growth of roadside trees in Seoul. Soil samples at $0{\sim}20\;cm$ depth and tree line were collected from Platanus occidentalis and Ginkgo biloba at nine streets, and pH and heavy Metal concentrations were analyzed. Soil pH ranged from 6.62 to 8.01 and soil heavy metal concentrations under roadside trees were higher (Zn 109.03, Pb 26.49 and Cu 44.98 mg/kg) compared with those of the referred forest soils. Soils at Cheonggye2ga street showed the highest heavy metal concentrations, and seemed to be related to heavy traffic and dense hardware stores. Tree ring width significantly decreased from 1979 through 2000 for both species. There were positive correlations between Cr, Pb and Cu concentrations in soils and tree ring layers for P. occidentalis and Ni for G. biloba. However, there were negative correlations between Cr concentration in tree ring layers and tree ring width for P. occidentalis, and Ni and Cu for G. biloba. Also there were no significant correlations between climatic factors in Seoul and tree ring width.