멀티미디어 동향과 가전

장규환,Jang, Gyu-Hwan 한국전자정보통신산업진흥회 1997 電子振興 Vol.17 No.10

Some examples of almost GCD-domains

장규환 충청수학회 2011 충청수학회지 Vol.24 No.3

Let D be an integral domain, X be an indeterminate over D,and D[X] be the polynomial ring over D. We show that D is an almost weakly factorial PvMD if and only if D+XD_S[X] is an integrally closed almost GCD-domain for each (saturated) multiplicative subset S of D, if and only if D+XD_1[X] is an integrally closed almost GCD-domain for any t-linked overring D_1of D, if and only if D_1+XD_2[X] is an integrally closed almost GCD-domain for all t-linked overrings D_1 ⊆ D_2 of D.

Graded integral domains in which each nonzero homogeneous ideal is divisorial

장규환,Haleh Hamdi,Parviz Sahandi 대한수학회 2019 대한수학회보 Vol.56 No.4

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 $S(H) = \{f \in R \,|\, C(f) = R\}$. 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\"ufer domain whose maximal ideals are invertible, if and only if $R$ satisfies the following four conditions: (i) $R$ is a graded-Pr\"{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.

COMPACTNESS OF A SUBSPACE OF THE ZARISKI TOPOLOGY ON SPEC(D)

장규환 호남수학회 2011 호남수학학술지 Vol.33 No.3

Let D be an integral domain, Spec(D) the set of prime ideals of D, and X a subspace of the Zariski topology on Spec(D). We show that X is compact if and only if given any ideal I of D with I ⊈ P for all P ∈ X, there exists a nitely generated ideal J ⊆ I such that J ⊈ P for all P ∈ X. We also prove that if D = ∩_(P∈X) D_P and if * is the star-operation on D induced by X, then X is compact if and only if * _f-Max(D) ⊆ X. As a corollary, we have that t-Max(D) is compact and that P(D) = {P ∈ Spec(D)|P is minimal over (a : b) for some a, b ∈ D} is compact if and only if t-Max(D) ⊆ P(D).

GRADED INTEGRAL DOMAINS AND PRUFER-LIKE DOMAINS

장규환 대한수학회 2017 대한수학회지 Vol.54 No.6

Let $R =\bigoplus_{\alpha \in \Gamma}R_{\alpha}$ 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 {\em upper to zero} in $R$ if $Q = fR_H \cap R$ for some $f \in R$ and that $R$ is a {\em 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 $\bar{R}_{H \setminus Q}$ is a graded-Pr\"ufer domain for all homogeneous maximal $t$-ideals $Q$ of $R$, if and only if $\bar{R}_{N(H)}$ is a Pr\"ufer domain, if and only if $R$ is a UMT-domain.

On t-almost Dedekind graded domains

장규환,오동렬 대한수학회 2017 대한수학회보 Vol.54 No.6

Let $\Gamma$ be a nonzero torsionless commutative cancellative \linebreak monoid with quotient group $\langle \Gamma \rangle$, $R = \bigoplus_{\alpha \in \Gamma}R_{\alpha}$ be a graded integral domain graded by $\Gamma$ such that $R_{\alpha} \neq \{0\}$ for all $\alpha \in \Gamma$, $H$ be the set of nonzero homogeneous elements of $R$, $C(f)$ be the ideal of $R$ generated by the homogeneous components of $f \in R$, and $N(H) = \{f \in R \mid C(f)_v = R\}$. In this paper, we introduce the notion of graded $t$-almost Dedekind domains. We then show that $R$ is a $t$-almost Dedekind domain if and only if $R$ is a graded $t$-almost Dedekind domain and $R_H$ is a $t$-almost Dedekind domains. We also show that if $R = D[\Gamma]$ is the monoid domain of $\Gamma$ over an integral domain $D$, then $R$ is a graded $t$-almost Dedekind domain if and only if $D$ and $\Gamma$ are $t$-almost Dedekind, if and only if $R_{N(H)}$ is an almost Dedekind domain. In particular, if $\langle \Gamma \rangle$ satisfies the ascending chain condition on its cyclic subgroups, then $R = D[\Gamma]$ is a $t$-almost Dedekind domain if and only if $R$ is a graded $t$-almost Dedekind domain.

Overrings of the Kronecker function ring Kr(D, *) of a Prüfer *-multiplication domain D

장규환 대한수학회 2009 대한수학회보 Vol.46 No.5

Let * be an e.a.b. star operation on an integrally closed domain D, and let Kr(D,*) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping Dα ↦ Kr(Dα, v) is a bijection from the set {Dα} of *-linked overrings of D into the set of overrings of Kr(D, v). This is a generalization of [5, Proposition 32.19] that if D is a Prüfer domain, then the mapping Dα↦ Kr(Dα, b) is a one-to-one mapping from the set {Dα} of overrings of D onto the set of overrings of Kr(D, b). Let * be an e.a.b. star operation on an integrally closed domain D, and let Kr(D,*) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping Dα ↦ Kr(Dα, v) is a bijection from the set {Dα} of *-linked overrings of D into the set of overrings of Kr(D, v). This is a generalization of [5, Proposition 32.19] that if D is a Prüfer domain, then the mapping Dα↦ Kr(Dα, b) is a one-to-one mapping from the set {Dα} of overrings of D onto the set of overrings of Kr(D, b).

특발망막전막에서 유리체절제술 후 유두황반신경섬유다발두께 변화에 대한 고찰

장규환,안자영,손준홍,황덕진 한국망막학회 2020 Journal of Retina Vol.5 No.2

Purpose: To observe changes in the papillomacular nerve fiber bundle (PMB) after pars plana vitrectomy (PPV) in patients with idiopathic epiretinal membrane (iERM) and to compare the surgical outcomes of PPV with and without air tamponade. Methods: From 2015 to 2017, medical records were retrospectively analyzed for patients who had received at least one year of follow- up after vitrectomy with iERM. Results: A total of 89 patients with 89 eyes were included in the study. In both groups (group with and without air tamponade) the mean best-corrected visual acuity (BCVA) after surgery improved significantly from 3 months to 1 year after surgery compared with preoperatively. The thickness of the PMB tended to increase gradually a month post-surgery; however, it showed a decline 3-months and 1-year post-operatively. The PMB thickness significantly increased until 6 months after surgery compared with the thickness of the opposite eye, but gradually decreased, and there was no significant difference at 1 year after surgery. There was no significant correlation between the thickness of the PMB and BCVA at 1 year postoperative. No difference between BCVA and PMB thickness was noted between the two groups at any point before or after the surgery. Conclusions: After vitrectomy in patients with iERM, PMB thickness increased temporarily and subsequently decreased, showing a significant difference at 3-months and 1-year post-surgery. However, PMB thickness did not show a significant difference compared with that of the opposite eye. BCVA improved significantly compared to its preoperative status, but there was no significant correlation between PMB thickness and BCVA 1-year postoperatively. Air tamponade did not significantly affect changes in visual acuity and PMB thickness during the 1 year postoperatively. 목적: 특발망막전막으로 유리체절제술을 받은 환자들에서 술 후 유두황반신경섬유다발(papillomacular nerve fiber bundle, PMB)의 변화를 관찰하고, 충전물에 의한 차이를 보이는지 확인하기 위해 안내 충전물을 공기로 시행한 군과 충전을 시행하지 않은 군으로 나누어 분석하였다. 대상과 방법: 2015년부터 2017년까지 특발망막전막으로 유리체절제술을 시행한 환자들 중 최소 1년간 경과 관찰을 한 환자들을 대상으로 의무기록을 후향적으로 분석하였다. 결과: 총 89명 89안이 포함되었으며, 두 군 전체에서 술 후 평균 시력은 술 전과 비교 시 3개월 이후부터 1년째까지 유의하게 호전되었고, PMB의 두께는 술 후 1개월까지 증가하다가 3개월 이후부터 1년까지 유의하게 감소하는 소견을 보였으며, 반대안의 PMB 두께와 비교 시 술 후 6개월까지는 유의하게 두께가 증가되어 있었지만 술 후 1년째에는 유의한 차이를 보이지 않았다. 또한, 두 군 모두 술 후 1년째 PMB의 두께와 최대교정시력 간에는 유의한 상관관계를 보이지 않았다. 두 군을 비교하였을 때, 시력과 PMB의 두께는 모든 시점에서 차이를 보이지 않았다. 결론: 특발망막전막으로 유리체절제술을 시행한 후 PMB는 술 후 3개월부터 1년째까지 유의하게 감소하였지만, 반대안과 비교 시 유의한 차이를 보이지는 않았다. 시력은 술 전과 비교 시 유의하게 호전되었으나, 술 후 1년째 PMB의 두께와는 유의한 상관관계를 보이지 않았다. 공기 충전은 술 후 1년 동안 시력 및 PMB 두께의 변화에 유의한 영향을 주지 않았다.

호서대학교 나노&바이오역학 연구실

장규환 한국소음진동공학회 2021 소음 진동 Vol.31 No.5

Graded integral domains and Nagata rings, II

장규환 강원경기수학회 2017 한국수학논문집 Vol.25 No.2

Let $D$ be an integral domain with quotient field $K$, $X$ be an indeterminate over $D$, $K[X]$ be the polynomial ring over $K$, and $R= \{f \in K[X] \mid f(0) \in D\}$; so $R$ is a subring of $K[X]$ containing $D[X]$. For $f = a_0 + a_1X + \cdots + a_nX^n \in R$, let $C(f)$ be the ideal of $R$ generated by $a_0, a_1X, \dots , a_nX^n$ and $N(H) = \{g \in R \mid C(g)_v = R\}$. In this paper, we study two rings $R_{N(H)}$ and Kr$(R, v) = \{\frac{f}{g} \mid f, g \in R$, $g \neq 0$, and $C(f) \subseteq C(g)_v\}$. We then use these two rings to give some examples which show that the results of [4] are the best generalizations of Nagata rings and Kronecker function rings to graded integral domains.