• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1499-1512
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• 2018

Recently, Anderson and Dumitrescu's S-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of S-finitely presented modules and then of S-coherent rings which are S-versions of finitely presented modules and coherent rings, respectively. Among other results, we give an S-version of the classical Chase's characterization of coherent rings. We end the paper with a brief discussion on other S-versions of finitely presented modules and coherent rings. We prove that these last S-versions can be characterized in terms of localization.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.961-976
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• 2019

Let R be any commutative ring and S be any multiplicative closed set. We introduce an S-version of $\mathcal{F}$-Mittag-Leffler modules, called $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and define the projective dimension with respect to these modules. We give some characterizations of $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, investigate the relationships between $\mathcal{F}$-Mittag-Leffler modules and $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and use these relations to describe noetherian rings and coherent rings, such as R is noetherian if and only if $R_S$ is noetherian and every $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler module is $\mathcal{F}$-Mittag-Leffler. Besides, we also investigate the $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension of R, and prove that $R_S$ is noetherian if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is zero; $R_S$ is coherent if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is at most one.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.29-40
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• 2024

Let S and R be rings and _SC_R a semidualizing bimodule. We introduce the notion of G_C-FP_n-injective modules, which generalizes G_C-FP-injective modules and G_C-weak injective modules. The homological properties and the stability of G_C-FP_n-injective modules are investigated. When S is a left n-coherent ring, several nice properties and new Foxby equivalences relative to G_C-FP_n-injective modules are given.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-10
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• 2021

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.

• Journal of architectural history
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• v.29 no.1
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• pp.21-37
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• 2020

The purpose of this paper is to reconstruct the original floor plan and wall design of Seokbulsa Grotto in Kyungju; commonly known as 'Seokguram'. The paper presents an array of dimensional studies of the existing Seokguram to examine its architectural form, and infers the original floor plan and wall design of Seokbulsa Grotto. Seokbulsa Grotto is designed as a system of 'coherent modules' and was constructed using the dry stone method, which interlocks large stone modules into a whole that becomes the load-bearing structure itself. The design principles governing Seokbulsa Grotto are the spatial axis of symmetry, modular coordination, and the layout grid of a quarter Tang-Ruler(TR: 唐尺). Dimensional studies were conducted with these governing principles in mind and concludes the following about the original floor plan design. In the main chamber, Ansang-stone's radius is 12 TR, and Flagstone's radius is 12¼ TR. In the front chamber, the width between the two Ansang-stones facing each other is 22 TR and the longitudinal space depth is 12 TR, while the width between the two Flagstones facing each other is 22½ TR and Flagstone's depth is 12 TR. In the passageway, the width between the two Ansang-stones facing each other is 11½ TR and longitudinal space depth is 9 TR, while the width between the two Flagstones facing each other is 12 TR and Flagstone's depth is 7¾ TR. The distance from the center to the entrance line of the main chamber is 10½ TR. Therefore, the total longitudinal length of the Grotto is 43½ TR at the level of the Ansang-stones, and 44 TR at the level of the Flagstones.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2003.10a
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• pp.164-169
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• 2003

In this paper, we propose the integrated Bayesian network framework to reconstruct genetic regulatory networks from genome expression data. The proposed model overcomes the dimensionality problem of multivariate analysis by building coherent sub-networks from confined gene clusters and combining these networks via intermediary points. Gene Shaving algorithm is used to cluster genes that share a common function or co-regulation. Retrieved clusters incorporate prior biological knowledge such as Gene Ontology, pathway, and protein protein interaction information for extracting other related genes. With these extended gene list, system builds genetic sub-networks using Bayesian network with MDL score and Sparse Candidate algorithm. Identifying functional modules of genes is done by not only microarray data itself but also well-proved biological knowledge. This integrated approach can improve there liability of a network in that false relations due to the lack of data can be reduced. Another advantage is the decreased computational complexity by constrained gene sets. To evaluate the proposed system, S. Cerevisiae cell cycle data [1] is applied. The result analysis presents new hypotheses about novel genetic interactions as well as typical relationships known by previous researches [2].