• 대한수학회지
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• 제54권6호
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• pp.1733-1757
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• 2017

Let $R={\oplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be an integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$, ${\bar{R}}$ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of $f{\in}R_H$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. Let $R_H$ be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if $Q=fR_H{\cap}R$ for some $f{\in}R$ and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of $R_{N(H)}$ is extended from a homogeneous ideal of R, if and only if ${\bar{R}}_{H{\backslash}Q}$ is a graded-$Pr{\ddot{u}}fer$ domain for all homogeneous maximal t-ideals Q of R, if and only if ${\bar{R}}_{N(H)}$ is a $Pr{\ddot{u}}fer$ domain, if and only if R is a UMT-domain.

• 대한수학회보
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• 제50권1호
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• pp.125-134
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• 2013

An element in a ring R is strongly clean provided that it is the sum of an idempotent and a unit that commutate. In this note, several necessary and sufficient conditions under which a $2{\times}2$ matrix over an integral domain is strongly clean are given. These show that strong cleanness over integral domains can be characterized by quadratic and Diophantine equations.

• 대한수학회보
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• 제55권1호
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• pp.187-204
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• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

• Journal of Microbiology and Biotechnology
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• 제13권2호
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• pp.263-268
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• 2003

Recently, we identified a domain, termed MIRC3-4, for the protein-protein interaction between yeast chitin synthase 3 (CHS3) and chitin synthase 4 (CHS4). In this study, the functional roles of MIRC3-4 were examined at the G1 phase and cytokinesis of the cell cycle by Calcofluor staining and FISH. Some mutations in MIRC3-4 resulted in disappearance of the chitin ring in the early G1 phase, but did not affect chitin synthesis in the cell wall at cytokinesis. The chitin distribution in chs4 mutant cells indicated that CHS4 was involved in the synthesis of chitinring in the G1 phase and in the synthesis of cell wall chitin after cytokinesis, suggesting that Chs4p regulates chitin synthase 3 activity differently in G1 and cytokinesis. Absence of the chitin ring could be caused either by delocalization of Chs3p to the bud-neck or by improper interaction with Chs4p. When mutant cells were immunostained with a Chs3p-specific antibody to discriminate between these two alternatives, the mutated Ch3p was found to localize to the neck in all MIRC3-4 mutants. These results strongly irdicate that Chs4p regulates Chs3p as an activator but not a recruiter.

• 대한수학회보
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• 제42권3호
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• pp.477-484
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• 2005

Let R be a ring with an automorphism 17. An ideal [ of R is ($\sigma$-ideal of R if $\sigma$(I).= I. A proper ideal P of R is ($\sigma$-prime ideal of R if P is a $\sigma$-ideal of R and for $\sigma$-ideals I and J of R, IJ $\subseteq$ P implies that I $\subseteq$ P or J $\subseteq$ P. A proper ideal Q of R is $\sigma$-semiprime ideal of Q if Q is a $\sigma$-ideal and for a $\sigma$-ideal I of R, I$^{2}$ $\subseteq$ Q implies that I $\subseteq$ Q. The $\sigma$-prime radical is defined by the intersection of all $\sigma$-prime ideals of R and is denoted by P$_{(R). In this paper, the following results are obtained: (1) For a principal ideal domain R, P$_{(R) is the smallest $\sigma$-semiprime ideal of R; (2) For any ring R with an automorphism $\sigma$ and for a skew Laurent polynomial ring R[x, x$^{-1}$; $\sigma$], the prime radical of R[x, x$^{-1}$; $\sigma$] is equal to P$_{(R)[x, x$^{-1}$; $\sigma$ ].

• 한국기계가공학회지
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• 제21권1호
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• pp.8-14
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• 2022

A computer simulation was performed to investigate the heat source distribution and temperature distribution of a laser having multiple characteristics. To simulate the actual size of a welding specimen, the temperature distributions at 0 s, 1 s, and 2 s were analyzed by increasing the domain size to 50 mm in length and 25 mm in width in a material of the same thickness. As indicated by the results, because of the characteristics of metals with high thermal conductivity, the temperature at the welding center line and the temperature distribution at the offset position were not significant. When the core part was cooled by irradiating with a laser, it cooled at a rate of up to 500 ℃/s. In contrast, when the laser was irradiated to the ring part, the cooling proceeded at a rate of over 1800 ℃/s. Comparing the relative numerical values rather than the absolute values, it was found that the cooling rate was approximately 3.6 times faster when the laser was irradiated through the ring than when the laser was irradiated through the core. As a result of irradiating with the same heat source (at 100 W) into the core, ring, and ring + core, it was confirmed that the highest temperature was irradiated to the ring part and the lowest temperature was irradiated to the core part.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.163-169
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• 2011

Let D be an integral domain, S be a multiplicative subset of D such that DS is a PID, and D[X] be the polynomial ring over D. We show that S is an almost splitting set in D if and only if every nonzero prime ideal of D disjoint from S contains a primary element. We use this result to give a simple proof of the known result that D is a UMT-domain and Cl(D[X]) is torsion if and only if each upper to zero in D[X] contains a primary element.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.371-379
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• 2012

Let D be an integral domain, $\bar{D}$ be the integral closure of D, * be a star operation of finite character on D, $*_w$ be the so-called $*_w$-operation on D induced by *, X be an indeterminate over D, $N_*=\{f{\in}D[X]{\mid}c(f)^*=D\}$, and $Kr(D,*)=\{0\}{\cup}\{\frac{f}{g}{\mid}0{\neq}f,\;g{\in}D[X]$ and there is an $0{\neq}h{\in}D[X]$ such that $(c(f)c(h))^*{\subseteq}(c(g)c(h))^*$}. In this paper, we show that D is a *-quasi-Pr$\ddot{u}$fer domain if and only if $\bar{D}[X]_{N_*}=Kr(D,*_w)$. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr$\ddot{u}$fer *-multiplication domain if and only if $D[X]_{N_*} = Kr(D,*_w)$.

• 대한수학회보
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• 제60권2호
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• pp.475-484
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• 2023

Let R be a commutative ring with identity. In this paper, we characterize the prime submodules of a free R-module F of finite rank with at most n generators, when R is a GCD domain. Also, we show that if R is a Bézout domain, then every prime submodule with n generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of F over a Bézout domain and characterize the minimal primary decomposition of this submodule.

• 한국미생물생명공학회:학술대회논문집
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• 한국미생물생명공학회 2002년도 학술발표대회
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• pp.18-25
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• 2002

The pikromycin biosynthetic system in Streptomyces venezuleae is unique for its ability to produce two groups of antibiotics that include the 12-membered ring macrolides methymycin and neomethymycin, and the 14-membered ring macrolides narbomycin and pikromycin. The metabolic pathway also contains two post polyketide-modification enzymes, a glycosyltransferase and P450 hydroxylase that have unusually broad substrate specificities. In order to explore further the substrate flexibility of these enzymes a series of hybrid polyketide synthases were constructed and their metabolic products characterized. The plasmid-based replacement of the multifunctional protein subunits of the pikromycin PKS in S. venezuelae by the corresponding subunits from heterologous modular PKSs resulted in recombinant strains that produce both 12- and 14-membered ring macrolactones with predicted structural alterations. In all cases, novel macrolactones were produced and further modified by the DesVII glycosyltransferase and PikC hydroxylase leading to biologically active macrolide structures. These results demonstrate that hybrid PKSs in S. venezuelae can produce a multiplicity of new macrolactones that are modified further by the highly flexible DesVII glycosyltransferase and PikC hydroxylase tailoring enzymes. This work demonstrates the unique capacity of the S. venezuelae pikromycin pathway to expand the toolbox of combinatorial biosynthesis and to accelerate the creation of novel biologically active natural products. The polyketide backbone of rifamycin B is assembled through successive condensation and ${\beta}$-carbonyl processing of the extender units by the modular rifamycin PKS. The eighth module, in the RifD protein, contains nonfunctional DH domain and functional KR domain, which specify the reduction of the ${\beta}$-carbonyl group resulting in the C-21 bydroxyl of rifamycin B. A four amino acid substitution and one amino acid deletion were introduced in the putative NADPH binding motif in the proposed KR domain encoded by rifD. This strategy of mutation was based on the amino acid sequences of the corresponding motif of the KR domain of module 3 in the RifA protein, which is believed dysfunctional, so as to introduce a minimum alteration and retain the reading frame intact, yet ensure loss of function. The resulting strain produces linear polyketides, from tetraketide to octaketide, which are also produced by a rifD disrupted mutant as a consequence of premature termination of polyketide assembly. Much of the structural diversity within the polyketide superfamily of natural products is due to the ability of PKSs to vary the reduction level of every other alternate carbon atom in the backbone. Thus, the ability to introduce heterologous reductive segments such as ketoreductase (KR), dehydratase (DH), and enoylreductase (ER) into modules that naturally lack these activities would increase the power of the combinatorial biosynthetic toolbox. The dehydratase domain of module 7 of the rifamycin PKS, which is predicted to be nonfunctional in view of the sequence of the apparent active site, was replaced with its functional homolog from module 7 of rapamycin-producing polyketide synthase. The resulting mutant strain behaved like a rifC disrupted mutant, i.e., it accumulated the heptaketide intermediate and its precursors. This result points out a major difficulty we have encountered with all the Amycolatopsis mediterranei strain containing hybrid polyketide synthases: all the engineered strains prepared so far accumulate a plethora of products derived from the polyketide chain assembly intermediates as major products instead of just analogs of rifamycin B or its ansamycin precursors.