• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.971-983
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• 2016

A partially ordered set P is ideal-homogeneous provided that for any ideals I and J, if $$I{\sim_=}_{\sigma}J$$, then there exists an automorphism ${\sigma}^*$ such that ${\sigma}^*{\mid}_I={\sigma}$. Behrendt [1] characterizes the ideal-homogeneous partially ordered sets of height 1. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and nd some families of ideal-homogeneous partially ordered sets.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.739-746
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• 2010

In this short paper, we show that properties of an ideal I of a ring R are related to those of the homogeneous ideal I(+)IM of a ring R(+)M.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1041-1057
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• 2019

Let ${\Gamma}$ be a nonzero commutative cancellative monoid (written additively), $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}$ $R_{\alpha}$ be a ${\Gamma}$-graded integral domain with $R_{\alpha}{\neq}\{0\}$ for all ${\alpha}{\in}{\Gamma}$, and $S(H)=\{f{\in}R{\mid}C(f)=R\}$. In this paper, we study homogeneously divisorial domains which are graded integral domains whose nonzero homogeneous ideals are divisorial. Among other things, we show that if R is integrally closed, then R is a homogeneously divisorial domain if and only if $R_{S(H)}$ is an h-local $Pr{\ddot{u}}fer$ domain whose maximal ideals are invertible, if and only if R satisfies the following four conditions: (i) R is a graded-$Pr{\ddot{u}}fer$ domain, (ii) every homogeneous maximal ideal of R is invertible, (iii) each nonzero homogeneous prime ideal of R is contained in a unique homogeneous maximal ideal, and (iv) each homogeneous ideal of R has only finitely many minimal prime ideals. We also show that if R is a graded-Noetherian domain, then R is a homogeneously divisorial domain if and only if $R_{S(H)}$ is a divisorial domain of (Krull) dimension one.

• Journal of Magnetics
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• v.17 no.2
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• pp.145-152
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• 2012

Patients who underwent hip arthroplasty using the conventional fat suppression technique (CHESS) and a new technique (IDEAL) were compared quantitatively to assess the effectiveness and usefulness of the IDEAL technique. In 20 patients who underwent hip arthroplasty from March 2009 to December 2010, fat suppression T2 and T1 weighted images were obtained on a 3.0T MR scanner using the CHESS and IDEAL techniques. The level of distortion in the area of interest, the level of the development of susceptibility artifacts, and homogeneous fat suppression were analyzed from the acquired images. Quantitative analysis revealed the IDEAL technique to produce a lower level of image distortion caused by the development of susceptibility artifacts due to metal on the acquired images compared to the CHESS technique. Qualitative analysis of the anterior area revealed the IDEAL technique to generate fewer susceptibility artifacts than the CHESS technique but with homogeneous fat suppression. In the middle area, the IDEAL technique generated fewer susceptibility artifacts than the CHESS technique but with homogeneous fat suppression. In the posterior area, the IDEAL technique generated fewer susceptibility artifacts than the CHESS technique. Fat suppression was not statistically different, and the two techniques achieved homogeneous fat suppression. In conclusion, the IDEAL technique generated fewer susceptibility artifacts caused by metals and less image distortion than the CHESS technique. In addition, homogeneous fat suppression was feasible. In conclusion, the IDEAL technique generates high quality images, and can provide good information for diagnosis.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.373-379
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• 2012

In this paper, we nd the inclusion relation among four categories of posets, i.e., ideal-homogeneous, tower-homogeneous, quasi-complement-preserved, and complement-preserved posets.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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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.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.429-436
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• 2009

In this short paper, we prove some new properties on homogeneous ideals and primary ideals of R(+)M.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.135-147
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• 1997

Let k be an infinite field and let $X = {P_1, \cdots, P_s}$ be a set of s-distinct points in $P^n$. We denote by $I(X)$ the defining ideal of $X$ in the polynomial ring $R = k[x_0, \cdots, x_n]$ and by A the homogeneous coordinate ring of $X, A = \sum_{t = 0}^{\infty} A_t$.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.675-684
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• 2017

Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study graded 2-absorbing primary and graded weakly 2-absorbing primary ideals of a graded ring which are different from 2-absorbing primary and weakly 2-absorbing primary ideals. We give some properties and characterizations of these ideals and their homogeneous components.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1319-1334
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• 2020

In this paper, we study the basic theory of the category of graded w-Noetherian modules over a graded ring R. Some elementary concepts, such as w-envelope of graded modules, graded w-Noetherian rings and so on, are introduced. It is shown that: (1) A graded domain R is graded w-Noetherian if and only if R^g_𝔪 is a graded Noetherian ring for any gr-maximal w-ideal m of R, and there are only finite numbers of gr-maximal w-ideals including a for any nonzero homogeneous element a. (2) Let R be a strongly graded ring. Then R is a graded w-Noetherian ring if and only if R_e is a w-Noetherian ring. (3) Let R be a graded w-Noetherian domain and let a ∈ R be a homogeneous element. Suppose 𝖕 is a minimal graded prime ideal of (a). Then the graded height of the graded prime ideal 𝖕 is at most 1.