• 대한수학회논문집
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• 제39권2호
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• pp.363-372
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• 2024

In this paper, we introduce a weak version of coherent that we call regular coherent property. A ring is called regular coherent, if every finitely generated regular ideal is finitely presented. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

• 대한수학회지
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• 제34권1호
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• pp.13-21
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• 1997

In recent years M. Hochster and C. Huneke introduced the notions of tight closure of an ideal and of the weak F-regularity of a ring of positive prime characteristic. Here 'F' stands for Frobenius. This notion enabled us to play an important role in a commutative ring theory, and other related topics.

• 한국조경학회지
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• 제22권2호
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• pp.13-24
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• 1994

the purpose of this study was to suggest managemental strategies for one-day use recreational area in public sector under competitive environment with private sector. Data was collected from citizens of Seoul, and 10 recreational areas were determined by a preliminary survey. Theses areas were regarded as "products", then positioning was applied to these products. Perceptual map was produced by multidimensional scaling to identify degree of competition among areas. Properties, which were developed by the Kelly Repertory Grid, were utilized to understand the strong and weak points of each area. Ideal types of recreational areas were analyzed by PREFMAP, then the size and distribution of recreation market of Seoul were found by grouping of individual ideal point by cluster analysis. Several strategies were suggested to enhance the competitive power for public recreation areas, and a few comments were described to improve this method for future research.

• 대한수학회보
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• 제53권5호
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• pp.1309-1325
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• 2016

This note focuses on a ring property in which upper and lower nilradicals coincide, as a generalizations of symmetric rings. The concept of symmetric ideal and ring in the noncommutative ring theory was initially introduced by Lambek, as an extension of the usual commutative ideal theory. The investigation of symmetric rings provided many useful results to the study in the noncommutative ring theory. So the results obtained from this study may be applicable to observing the structure of zero divisors in various kinds of algebraic systems containing matrix rings and polynomial rings.

• 대한수학회보
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• 제58권4호
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• pp.1039-1052
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• 2021

In this paper, we introduce and study the class of 𝜙-w-flat modules which are generalizations of both 𝜙-flat modules and w-flat modules. The 𝜙-w-weak global dimension 𝜙-w-w.gl.dim(R) of a commutative ring R is also introduced and studied. We show that, for a 𝜙-ring R, 𝜙-w-w.gl.dim(R) = 0 if and only if w-dim(R) = 0 if and only if R is a 𝜙-von Neumann ring. It is also proved that, for a strongly 𝜙-ring R, 𝜙-w-w.gl.dim(R) ≤ 1 if and only if each nonnil ideal of R is 𝜙-w-flat, if and only if R is a 𝜙-PvMR, if and only if R is a PvMR.

• 대한수학회보
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• 제60권6호
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• pp.1687-1695
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• 2023

In this paper, we study the Green ring r(𝔴⁰_n) of the weak Hopf algebra 𝔴⁰_n based on Taft Hopf algebra H_n(q). Let R(𝔴⁰_n) := r(𝔴⁰_n) ⊗_ℤ ℂ be the Green algebra corresponding to the Green ring r(𝔴⁰_n). We first determine all finite dimensional simple modules of the Green algebra R(𝔴⁰_n), which is based on the observations of the roots of the generating relations associated with the Green ring r(𝔴⁰_n). Then we show that the nilpotent elements in r(𝔴⁰_n) can be written as a sum of finite dimensional indecomposable projective 𝔴⁰_n-modules. The Jacobson radical J(r(𝔴⁰_n)) of r(𝔴⁰_n) is a principal ideal, and its rank equals n - 1. Furthermore, we classify all finite dimensional non-simple indecomposable R(𝔴⁰_n)-modules. It turns out that R(𝔴⁰_n) has n² - n + 2 simple modules of dimension 1, and n non-simple indecomposable modules of dimension 2.

• 대한수학회논문집
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• 제18권1호
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• pp.59-63
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• 2003

Let A be a $C^*$-algebra and $K_{A}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\Gamma(K_{A})\;of\;K_{A}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\Gamma(K_{A})$.

• 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.

• 한국자기공명학회:학술대회논문집
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• 한국자기공명학회 2002년도 International Symposium on Magnetic Resonance
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• pp.70-71
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• 2002

Exchange-coupled cluster of transition-metal ions are relevant to many different scientific areas, ranging from chemistry to solid-state physics, biology, material science and has been the subject of much research in recent years(1,2). Single crystal EPR spectroscopy works as a very effective tool for the measurement of J values for small exchange interactions. This makes EPR technique very suitable for detection of weak exchange coupling transmitted over long distances via extended atomic and melecular bridges. Large polyoxometallates (3) may provide ideal structural environments for the study of interactions between paramagnetic ions. The detailed nature of magnetic interaction (positive sign and magnitude of J~0.006 $cm^{-1}$ /) was clearly determined for di-copper(II) system by single crystal EPR spectroscopy (4). The single-triplet (S-T) transitions are forbidden by different symmetries of the wave functions. However, when the singlet ground state is mixed into triplet states, the S-T transitions can be allowed and observed as weak lines. These weak S-T lines are positioned symmetrically with respect to the main transitions in the distance equals to 2J from the center of the spectrum. This lines allow one to determine the J-value with very high accuracy when │J│ ＜ hv 0.32 $cm^{-1}$ /. Unfortunately, the S-T transitions in the single crystal were detected by EPR method only in a few complexes until now. We have measured single-triplet transition lines for several magnetically coupled cluster systems and determined their J values accurately. The temperature dependency of J was studied by monitoring the changes in S-T.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권4호
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• pp.1760-1778
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• 2018

For image segmentation with intensity inhomogeneity, many region-based level set methods have been proposed. Some of them however can't get the relatively ideal segmentation results under the severe intensity inhomogeneity and weak edges, and without use of the image gradient information. To improve that, we propose a new level set method combined with local direction gradient in this paper. Firstly, based on two assumptions on intensity inhomogeneity to images, the relationships between segmentation objects and image gradients to local minimum and maximum around a pixel are presented, from which a new pixel classification method based on weight of Euclidian distance is introduced. Secondly, to implement the model, variational level set method combined with image spatial neighborhood information is used, which enhances the anti-noise capacity of the proposed gradient information based model. Thirdly, a new diffusion process with an edge indicator function is incorporated into the level set function to classify the pixels in homogeneous regions of the same segmentation object, and also to make the proposed method more insensitive to initial contours and stable numerical implementation. To verify our proposed method, different testing images including synthetic images, magnetic resonance imaging (MRI) and real-world images are introduced. The image segmentation results demonstrate that our method can deal with the relatively severe intensity inhomogeneity and obtain the comparatively ideal segmentation results efficiently.