• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.1-10
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• 2011

Let (R, T) be a normal pair of commutative rings (i.e., R ${\subseteq}$ T is a unita extension of commutative rings, not necessarily integral domains, such that S is integrally closed in T for each ring S such that R ${\subseteq}$ S ${\subseteq}$ T) such that the total quotient ring of R is a von Neumann regular ring. Let P be one of the following ring-theoretic properties: going-down ring, extensionally going-down (EGD) ring, locally divided ring. Then R has P if and only if T has P. An example shows that the "if" part of the assertion fails if P is taken to be the "divided domain" property.

• 대한수학회보
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• 제59권1호
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• pp.213-226
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• 2022

Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the natural homomorphism I ⊗_R M → R ⊗_R M is a w-monomorphism for any regular ideal I. We distinguish regular w-flat modules from regular flat modules and w-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Prüfer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.817-826
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• 2015

Let R be a commutative ring with total quotient ring K. Each monomorphic R-module endomorphism of a cyclic R-module is an isomorphism if and only if R has Krull dimension 0. Each monomorphic R-module endomorphism of R is an isomorphism if and only if R = K. We say that R has property (${\star}$) if for each nonzero element $a{\in}R$, each monomorphic R-module endomorphism of R/Ra is an isomorphism. If R has property (${\star}$), then each nonzero principal prime ideal of R is a maximal ideal, but the converse is false, even for integral domains of Krull dimension 2. An integral domain R has property (${\star}$) if and only if R has no R-sequence of length 2; the "if" assertion fails in general for non-domain rings R. Each treed domain has property (${\star}$), but the converse is false.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.271-275
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• 2010

Let R be a commutative ring with identity, T(R) be the total quotient ring of R, and D be a ring such that $R{\subseteq}D{\subseteq}T(R)$ and D is a finite R-module. In this paper, we show that each regular ideal of R is finitely generated if and only if each regular ideal of D is finitely generated. This is a generalization of the Eakin-Nagata theorem that R is Noetherian if and only if D is Noetherian.

• 대한수학회지
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• 제51권3호
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• pp.509-525
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• 2014

Let R be a commutative ring with identity. An R-module M is said to be w-projective if $Ext\frac{1}{R}$(M,N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w-semi-hereditary if every finite type ideal of R is w-projective. To characterize w-semi-hereditary rings, we introduce the concept of w-injective modules and study some basic properties of w-injective modules. Using these concepts, we show that R is w-semi-hereditary if and only if the total quotient ring T(R) of R is a von Neumann regular ring and $R_m$ is a valuation domain for any maximal w-ideal m of R. It is also shown that a connected ring R is w-semi-hereditary if and only if R is a Pr$\ddot{u}$fer v-multiplication domain.

• 대한수학회보
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• 제52권3호
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• pp.935-946
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• 2015

The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be ${\phi}$-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map ${\phi}$ from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a ${\phi}$-ring R is said to be a ${\phi}$-pseudo-strongly prime ideal if, whenever $x,y{\in}R_{Nil(R)}$ and $(xy){\phi}(P){\subseteq}{\phi}(P)$, then there exists an integer $m{\geqslant}1$ such that either $x^m{\in}{\phi}(R)$ or $y^m{\phi}(P){\subseteq}{\phi}(P)$. If each prime ideal of R is a ${\phi}$-pseudo strongly prime ideal, then we say that R is a ${\phi}$-pseudo-almost valuation ring (${\phi}$-PAVR). Among the properties of ${\phi}$-PAVRs, we show that a quasilocal ${\phi}$-ring R with regular maximal ideal M is a ${\phi}$-PAVR if and only if V = (M : M) is a ${\phi}$-almost chained ring with maximal ideal $\sqrt{MV}$. We also investigate the overrings of a ${\phi}$-PAVR.

• 대한수학회논문집
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• 제35권4호
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• pp.1095-1106
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• 2020

The purpose of this paper is to introduce a new class of rings that is closely related to the class of pseudo-Krull domains. Let 𝓗 = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. Let R ∈ 𝓗 be a ring with total quotient ring T(R) and define 𝜙 : T(R) → R_Nil(R) by ${\phi}({\frac{a}{b}})={\frac{a}{b}}$ for any a ∈ R and any regular element b of R. Then 𝜙 is a ring homomorphism from T(R) into R_Nil(R) and 𝜙 restricted to R is also a ring homomorphism from R into R_Nil(R) given by ${\phi}(x)={\frac{x}{1}}$ for every x ∈ R. We say that R is a 𝜙-pseudo-Krull ring if 𝜙(R) = ∩ R_i, where each R_i is a nonnil-Noetherian 𝜙-pseudo valuation overring of 𝜙(R) and for every non-nilpotent element x ∈ R, 𝜙(x) is a unit in all but finitely many R_i. We show that the theories of 𝜙-pseudo Krull rings resemble those of pseudo-Krull domains.

• Journal of the Korean Wood Science and Technology
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• 제31권6호
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• pp.31-39
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• 2003

The enzymatic isolation of residual lignins obtained from spruce and beech pulps (obtained by sulfite, kraft, ASAM and soda/AQ/MeOH pulping processes) and their characterization was described in previous publications. Here, the residual lignins have been submitted to potassium permanganate oxidation (KMnO₄ degradation), and 9 aromatic carboxylic acids (3 of them are dimeric) were identified after methylation with diazomethane by GC/MS. The analytical challenge during qantification by the internal standard methods was the partly high protein content of the samples, which resulted in elevated anisic acid yields in the degradation mixture of sulfite residual lignins. The results are compared with the KMnO₄ degradation of the corresponding MWLs and discussed in terms of S/G ratios and degrees of condensation. The latter was calculated as a quotient between the aromatic carboxylic acids derived from condensed and non-condensed lignin structures. Typical degradation patterns for the various processes have been observed. Among other parameter, the relative compositions between iso-hemipinic acid (which is for condensation in pos. 5 of the aromatic ring) and meta-hemipinic acid and 3,4,5-trimethoxyphthalic acid (both are for condensation in pos. 6 of the aromatic ring) was found to be process specific. Kraft and soda/AQ/MeOH residual lignins yielded higher amounts of iso-hemipinic acid. In contrast, the relative yields of meta-hemipinic acid and 3,4,5-trimethoxyphthalic acid (the latter in beech lignins) are higher in sulfite and particularly in ASAM residual lignin. In case of beech residual lignins the amount of acids originated from non-condensed syringyl type lignin units was surprisingly high. The condensation degree of residual lignins was shown to be generally higher than that of MWLs. This was especially true for the G units. ASAM residual lignin exhibited very high S/G ratios and degrees of polymerization. Causality between condensation degree and total yield of degradation products was demonstrated.

• 대한지리학회지
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• 제30권1호
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• pp.68-92
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• 1995

소매업은 경제, 사회, 문화, 정치를 배경으로 소비자의 요구에 부응하며 발전해 가 기 때문에 지역구조의 이해라는 측면에서 증요한 연구 주제이다. 또한 소매업은 일상생활을 영위하기 위한 기본적인 기능이므로, 이에 대한 이해는 삶의 질 향상이라는 측면에서도 중 요하다. 최근, 우리나라는 주민소득의 향상과 그에 따른 수요의 다양화, 개성화, 그리고 정보 화 사회로의 이행, 대기업 및 외국유통업의 참여, 정부의 유통산업 근대화 작업 등 소매업 환경의 변화와 함께 소매업이 크게 변화하고 있다. 따라서 미래의 변화 예측과 바람직한 발 전 방향이 제시되어야 함에도 불구하고, 이에 대한 연구가 미흡하다. 이에 광주시를 연구대 상지역으로 선정하여, 소매업의 입지와 그에 대한 주민의 이용 행태, 그리고 주민의 바람직 한 이용방안을 분석하였다. 이는 입지행태라는 순수한 학문적기여 뿐 아니라, 지역의 효율성 과 평등성의 실현이라는 응용면에서도 중요한 의의를 지닌다.