• Kyungpook Mathematical Journal
• /
• v.51 no.1
• /
• pp.1-10
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.213-226
• /
• 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
• /
• v.55 no.4
• /
• pp.817-826
• /
• 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
• /
• v.18 no.3
• /
• pp.271-275
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.509-525
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.935-946
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1095-1106
• /
• 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
• /
• v.31 no.6
• /
• pp.31-39
• /
• 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.

• Journal of the Korean Geographical Society
• /
• v.30 no.1
• /
• pp.68-92
• /
• 1995

Recentry the structure of the retail trade have been chanaed with its environmantal changes. Some studies may be necessary on the changing process of environment and fundamental structure analyses of the retail trade. This study analyzes the location of retail trades, inhabitants' behavior in retail tredes and their desirable utilization scheme of them in Kwangju-si. Some study methods, contents and coming-out results are as follows: 1. Retail trades can be classified into independent stores, chain-stores (supermarket, voluntary chain and frenchiise system and convenience store), department stores, cooperative associations, traditional, markets mail-order marketing, automatic vending and others by service levels, selling-items, prices, managements, methods of retailing and store or nonstore type. 2. In Kwangju, the environment of retail trades is related to the consumers of population structure: chanes in consumers pattern, trends toward agings and nuclear family, increase of leisur: time and female advances to society. Rapid structural shift in retail trade has also been occurred due to these social changes. Traditionl and premodern markets until 1970s altere to supermarkets or department stores in 1980s, and various types, large enterprises and foreign capitals came into being in 1990s. 3. The locational characteristics of retail trades are resulted from the spatial analysis of the total population distribution, and from the calculation of segregation index in the light of potential demand. The densely-populated areas occurs in newly-built apartment housing complex which is distributed with a ring-shaped pattern around the old urban core. The numbers and rates of the aged over sixty in Kwangsan-gu and the circumference area of Mt.Moodeung, are larger and higher where rural elements are remarkable. A relation between population distribution and retail trade are analysed by the index of population per shop. The index of the population number per shop is lower in urban center, as a whole, being more convenient for consumers. In newly-formed apartment complex areas, on the other, the index more than 1,000 per shop, meeting not the demands for consumers. Because both the younger and the aged are numerous in these areas, the retail trade pattern pertinent to both are needed. Urban fringes including Kwangsan-gu and the vicinity of Mt.Moodeung have some problems owing to the most of population number per shop (more than 1, 500) and the most extensive as well. 4. The regional characteristic of retail trade is analyzed through the location quotient of shops by locational patterns and centerality index. Chungkum-dong is the highest-order central place in CBD. It is the core of retail trades, which has higher-ordered specialty store including three big department stores, supermarkets and large stores. Taegum-dong, Chungsu-dong, Taeui-dong, and Numun-dong that are neiahbored to Chungkum-dong fall on the second group. They have a central commercial section where large chain stores, specialty shopping streets, narrow-line retailing shops (furniture, amusement service, and gallary), supermarkets and daily markets are located. The third group is formed on the axis of state roads linking to Naju-kun, Changseong-kun, Tamyang-kun, Hwasun-kun and forme-Songjeong-eup. It is related to newly, rising apartment housing complex along a trunk road, and characterized by markets and specialty stores. The fourth group has neibourhood-shopping centers including older residential area and Songjeong-eup area with independent stores and supermarkets as main retailing functions. The last group contains inner residential area and outer part of a city including Songjeong-eup. Outer part of miscellaneous shops being occasionally found is rural rather than urban (Fig. 7). 5. The residents' behaviors using retail trade are analyzed by factors of goods and facilities. Department stores are very high level in preference for higher-order shopping-goods such as clothes for full dress in view of both diversity and quality of goods(28.9%). But they have severe traffic congestions, and high competitions for market ranges caused by their sma . 64.0% of respondents make combined purpose trips together with banking and shopping. 6. For more efficiency of retail-trading, it is necessary to induce spatial distribution policy with regard to opportunity frequency of goods selection by central place, frontier regions and age groups. Also we must consider to analyze competition among different types of retail trade and analyze the consumption behaviors of working females and younger-aged groups, in aspects of time and space. Service improvement and the rationalization of management should be accomplished in such as cooperative location (situation) must be under consideration in relations to other functions such as finance, leisure & sports, and culture centers. Various service systems such as installment, credit card and peremium ticket, new used by enterprises, must also be carried service improvement. The rationalization and professionalization in for the commercial goods are bsically requested.