• Honam Mathematical Journal
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• v.30 no.1
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• pp.91-99
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• 2008

Let R be a commutative ring (with identity). In this paper we will obtain some results concerning comultiplication R-modules. Further we state and prove a dual notion of Nakayama's lemma for finitely cogenerated modules.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.803-808
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• 2007

In present article, we consider the embeddability problems for finite dimensional irreducible modules over a complex simple Lie algebra L. For s1(n,C) modules, we determine when one can be embedded into the other if s1(n,C) modules are tensor products of fundamental modules.

• Journal of Korean Elementary Science Education
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• v.27 no.1
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• pp.83-92
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• 2008

In this study, we developed elementary science education modules for facilitating students' understanding of the connected nature of Science-Technology-Society. For these modules, we particularly used news articles to make connections among science, technology, and society. We set up the development criteria as followings: connecting science-technology-society, aligning with national science curriculum, respecting students' interest, and appropriating the difficulty levels in terms and concepts. We also studied 4th grade students' perception of using these modules in science lessons. Most students perceived that using the modules in their science classes helped them link science-technology-society intimately and enhance their interest and motivation, as well as their self-esteem for studying science.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.691-707
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• 2020

In this paper, we introduce and study the notions of weakly ⊕-supplemented modules, weakly D2 modules and weakly D2-covers. A right R-module M is called weakly ⊕-supplemented if every non-small submodule of M has a supplement that is not essential in M, and module M_R is called weakly D2 if it satisfies the condition: for every s ∈ S and s ≠ 0, if there exists n ∈ ℕ such that sⁿ ≠ 0 and Im(sⁿ) is a direct summand of M, then Ker(sⁿ) is a direct summand of M. The class of weakly ⊕-supplemented-modules and weakly D2 modules contains ⊕-supplemented modules and D2 modules, respectively, and they are equivalent in case M is uniform, and projective, respectively.

• Journal of The Korean Association For Science Education
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• v.25 no.7
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• pp.754-764
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• 2005

The purpose of this study was to develop experimental modules that would enhance science the process skills of secondary school students. The modules were composed of real-life materials on the subjects of light, movement, force, water, and heat. Each module consisted of four to six activities, and provided student worksheets and teacher guides. Physics teachers were invited to a workshop specially held to identify whether these modules would befit the improvement of student science process skills. A majority of the teachers believed the modules to be valuable instructional materials which might enhance student science process skills in the Korean secondary school science classes.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1563-1567
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• 2021

We show that if M is a Utumi module, in particular if M is quasi-continuous, then M = Q ⊕ K, where Q is quasi-injective that is both a square-full as well as a dual-square-full module, K is a square-free module, and Q & K are orthogonal. Dually, we also show that if M is a dual-Utumi module whose local summands are summands, in particular if M is quasi-discrete, then M = P ⊕ K where P is quasi-projective that is both a square-full as well as a dual-square-full module, K is a dual-square-free module, and P & K are factor-orthogonal.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.85-90
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• 1991

In this article we introduce the readers to the theory of Carlitz modules which are rank one Drinfeld modules. The main point is the striking similarities between cyclotomic number fields and Carlitz modules.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1061-1078
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• 2020

We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog's generalized local cohomology modules.

• Journal of the Korean earth science society
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• v.27 no.7
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• pp.715-722
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• 2006

This study intended to find evidence of changes in teacher beliefs of teaching and learning and a case of infusing research experiences in teaching modules since their research participation. As part of this study, twenty three science and math teachers in Korea were provided with science research labs and field experiences in the University of Iowa for three weeks. The research units that teachers participated in for three weeks covered seven fields of subjects such as: geology, astronomy, chemistry, physics, mathematics, computer science, and environmental engineering. In the course of this study, the effectiveness of science research participation program was explored in terms of changing teacher beliefs and their production of teaching modules based on their research. This study especially focused on identifying changes of beliefs on science teaching and learning after participating in the research. A case study of a participant teacher was also conducted by comparing descriptively teaching modules before and after experiencing the program. It was found that the program affected the new modules and the research experiences affected participants' beliefs toward student centeredness.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.895-903
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• 2023

In this paper, we give some results on 2-strongly Gorenstein projective modules and related rings. We first investigate the relationship between strongly Gorenstein projective modules and periodic modules and then give the structure of modules over strongly Gorenstein semisimple rings. Furthermore, we prove that a ring R is 2-strongly Gorenstein hereditary if and only if every ideal of R is Gorenstein projective and the class of 2-strongly Gorenstein projective modules is closed under extensions. Finally, we study the relationship between 2-Gorenstein projective hereditary and 2-Gorenstein projective semisimple rings, and we also give an example to show the quotient ring of a 2-Gorenstein projective hereditary ring is not necessarily 2-Gorenstein projective semisimple.