• 호남수학학술지
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• 제30권1호
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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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• 제18권3호
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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.

• 한국초등과학교육학회지:초등과학교육
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• 제27권1호
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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.

• 대한수학회보
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• 제57권3호
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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.

• 한국과학교육학회지
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• 제25권7호
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• pp.754-764
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• 2005

이 연구는 증등학생의 탐구능력 향상을 위한 실생활 소재 탐구모듈 개발 연구이다. 실생활소재를 사용하여 물, 열, 빛, 운동, 물질과 관련된 물리내용으로 모듈을 구성하였는데, 각 모듈 당 4-6개의 관련 활동들이 포함되어 있고, 각 모듈은 학생용 실험서와 교사용 지도서로 구성되어 있다. 모듈을 현장 물리 교사에게 워크삽을 통해 모듈의 목표, 내용, 활용 측면에서 타당도 평가를 받았는데, 모듈의 목표 측면에서는 79%의 긍정적인 평가를 받았고, 내용 측면에서는 77%, 활용 측면에서는 71 %의 긍정적인 평가를 받아, 전체적으로 74 %의 긍정적인 평가를 받았으며, 모듈의 개선점, 보완점등의 설문을 바탕으로 수정보완하여 모듈을 완성하였다.

• 대한수학회보
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• 제58권6호
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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.

• 충청수학회지
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• 제4권1호
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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.

• 대한수학회지
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• 제57권5호
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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.

• 한국지구과학회지
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• 제27권7호
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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.

• 대한수학회보
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• 제60권4호
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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.