• Honam Mathematical Journal
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• v.45 no.2
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• pp.269-284
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• 2023

In this paper we study generalizations of the concept of pure-direct-projectivity from module categories to Grothendieck categories. We examine for which categories or under what conditions pure-direct-projective objects are direct-projective, quasi-projective, pure-projective, projective and flat. We investigate classes all of whose objects are pure-direct-projective. We give applications of some of the results to comodule categories.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1389-1406
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• 2020

Let Λ be an Artin algebra and mod Λ the category of finitely generated right Λ-modules. We prove that the radical layer length of Λ is an upper bound for the radical layer length of mod Λ. We give an upper bound for the extension dimension of mod Λ in terms of the injective dimension of a certain class of simple right Λ-modules and the radical layer length of DΛ.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.527-539
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• 1995

We consider the Schur groups of some module categories, which are subcategories of category of divisorial modules over a Krull domain. Then we obtain the exact sequence connecting class group, Schur class group and Schur groups of these categories.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.733-756
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• 2022

In this paper, we introduce the notion of Gorenstein quasiresolving subcategories (denoted by 𝒢𝒬𝓡_𝒳 (𝓐)) in term of quasi-resolving subcategory 𝒳. We define a resolution dimension relative to the Gorenstein quasi-resolving categories 𝒢𝒬𝓡_𝒳 (𝓐). In addition, we study the stability of 𝒢𝒬𝓡_𝒳 (𝓐) and apply the obtained properties to special subcategories and in particular to modules categories. Finally, we use the restricted flat dimension of right B-module M to characterize the finitistic dimension of the endomorphism algebra B of a 𝒢𝒬_𝒳-projective A-module M.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.439-458
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• 2018

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category C of groups with operations using the categorical equivalence between the categories of crossed modules and of internal categories in C. Further, we characterize the derivations of crossed modules in a category C and obtain new crossed modules using regular derivations of old one.

• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1337-1364
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• 2023

We describe the Gorenstein derived categories of Gorenstein rings via the homotopy categories of Gorenstein injective modules. We also introduce the concept of Gorenstein cosilting complexes and study its basic properties. This concept is generalized by cosilting complexes in relative homological methods. Furthermore, we investigate the existence of the relative version of the Bongartz's theorem and construct a Bongartz's complement for a Gorenstein precosilting complex.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.9-22
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• 2014

In this paper we state some applications of Gr-category theory to the classification problem of crossed modules and to that of group extensions of the type of a crossed module.

• The KIPS Transactions:PartD
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• v.11D no.4
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• pp.799-808
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• 2004

Well documented, simplified and clarified source code is required for the mission critical application software area in which C programing language is generally used. We suggest an XML_based comment management system for C source code. The comment management system is composed of 6 modules including comment user module, reviewer module, comment extraction module, comment traceability link module, comment tag definition module and storage management module. The XML comment tags defined in this paper cover categories of the development process activities applying the IEEE standard 1028 and IEEE standard 1012. The XML Schema Is used to insert comments into C source code and to extract XML tags from C source code and the XSL-FO is used fur the visual display professing o( comment extraction results.

• 한국지구과학회:학술대회논문집
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• 2005.09a
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• pp.304-314
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• 2005

The present study aims to develop animation module-based teaching-learning materials for a unit of middle school 3rd grade science, which contains the movement of the solar system, through the utilization of various forms of multimedia elements. The developed materials consist of 12 in total flash animation modules covering ‘movement of the Earth,’ ‘movement of the Moon,’ movement of the Planets,‘ etc. To analyze the student responses to the science classes to which the developed animation modules were to be applied, the researcher selected for subjects two third-grade classes that were made up of 60 students and later divided for an experimental group and a control group in a middle school located in Jeonju. The experimental group was treated with the animation module-based lessons developed in the present study while the control group was taught in the traditional teacher-centered ways. Tests for the science-related attitudes of the two groups were administered and the results showed that the mean score of the experimental group was significantly higher than the mean score of the control group (p<0.05) in the categories of ‘interest’ and ‘scientific attitude’. It was thus believed that the animation module-based teaching has a positive effect on the categories of ‘interest’ and ‘scientific attitude’. To assess the qualitative dimension of the developed materials, the researcher subjected them to the utilization of the 30 local science teachers and afterwards a survey was done with the 8 crucial items taken from the WBI evaluation test developed by Multimedia Education Support Center in 1998. The result was broadly positive in terms of lesson design and from a technological point of view.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.151-163
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• 2019

The aim of this paper is to consider the categorical equivalence between crossed modules within groupoids and 2-groupoids; and then relate normality and quotient in these two categories.