• 대한수학교육학회지:학교수학
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• 제7권4호
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• pp.403-425
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• 2005

본 연구는 네덜란드의 초등 교육과정에 대한 문헌 연구를 통해 RME에 기초한 초등 수학교육의 실제를 자연수와 연산 영역을 중심으로 구체적으로 알아보고 우리나라 교육과정과 교과서 개발을 위한 시사점을 도출하는 데 그 목적이 있다. 이러한 목적을 달성하기 위해 네덜란드의 초등 교육과정에 결정적인 영향을 미치는 요소인 핵심 목표, 네덜란드의 교과서, TAL 프로젝트의 결과물인 초등학교 학생들의 거시적인 교수 학습 경로를 살펴보았다. 그 결과 RME에 기초한 초등 수학교육은 현실 상황의 주제 중심의 통합형 교육과정이며, 자연수와 연산 영역 지도의 특징으로는 수세기, 상황화, 위치화, 구조화, 수준에 기초한 점진적 알고리즘화, 어림의 강조와 계산기의 적절한 사용을 강조하고 있음을 알 수 있었다. 이를 바탕으로 앞으로의 교육과정과 교과서 개발을 위해 논의할 문제로 수 개념 지도에서 농도수와 순서수 지도의 균형, 수의 상대적 크기의 지도, 다양한 연산 전략의 지도, 다양한 교수학적 모델의 사용을 제안하였다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권1호
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• pp.51-66
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• 2012

This study investigated the impact of entry level of mathematics subject knowledge on student teachers' mathematics pedagogical content knowledge development and performance in mathematics teaching practice. The sample consisted of 24 mathematics student teachers, 12 of whom passed A-Level mathematics and 12 of whom only passed O-level mathematics. They were all studying in a 4-year bachelor of education (Honours/Primary) programme; they were either majoring or minoring in mathematics. Results showed that student teachers' entry-level mathematics subject knowledge is not related to their mathematics pedagogical content knowledge development or their mathematics teaching performance. These findings may lead society to consider whether student teachers who have passed O-level mathematics are already eligible to be trained as professional primary mathematics teachers. As a consequence, this study raises the issues of how to develop student teachers' mathematics pedagogical content knowledge and whether we need to restructure our bachelor of education (Primary) programmes' curriculum in teacher professionalism.

• 대한수학회지
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• 제52권1호
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• pp.97-111
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• 2015

Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, $c{\in}R$ and $0{\neq}abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.

• 대한수학회보
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• 제51권4호
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• pp.1163-1173
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• 2014

Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever $a,b,c{\in}R$ and $abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.

• 대한수학회보
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• 제58권5호
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• pp.1069-1078
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• 2021

Let R be a commutative ring with identity. A proper ideal I of R is called 1-absorbing primary ([4]) if for all nonunit a, b, c ∈ R such that abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. The concept of 1-absorbing primary ideals in a polynomial ring, in a PID and in idealization of a module is studied. Moreover, we introduce weakly 1-absorbing primary ideals which are generalization of weakly prime ideals and 1-absorbing primary ideals. A proper ideal I of R is called weakly 1-absorbing primary if for all nonunit a, b, c ∈ R such that 0 ≠ abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. Some properties of weakly 1-absorbing primary ideals are investigated. For instance, weakly 1-absorbing primary ideals in decomposable rings are characterized. Among other things, it is proved that if I is a weakly 1-absorbing primary ideal of a ring R and 0 ≠ I₁I₂I₃ ⊆ I for some ideals I₁, I₂, I₃ of R such that I is free triple-zero with respect to I₁I₂I₃, then I₁I₂ ⊆ I or I₃ ⊆ I.

• 대한수학회보
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• 제56권3호
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• pp.729-743
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• 2019

In this paper, we introduce strongly quasi primary ideals which is an intermediate class of primary ideals and quasi primary ideals. Let R be a commutative ring with nonzero identity and Q a proper ideal of R. Then Q is called strongly quasi primary if $ab{\in}Q$ for $a,b{\in}R$ implies either $a^2{\in}Q$ or $b^n{\in}Q$ ($a^n{\in}Q$ or $b^2{\in}Q$) for some $n{\in}{\mathbb{N}}$. We give many properties of strongly quasi primary ideals and investigate the relations between strongly quasi primary ideals and other classical ideals such as primary, 2-prime and quasi primary ideals. Among other results, we give a characterization of divided rings in terms of strongly quasi primary ideals. Also, we construct a subgraph of ideal based zero divisor graph ${\Gamma}_I(R)$ and denote it by ${\Gamma}^*_I(R)$, where I is an ideal of R. We investigate the relations between ${\Gamma}^*_I(R)$ and ${\Gamma}_I(R)$. Further, we use strongly quasi primary ideals and ${\Gamma}^*_I(R)$ to characterize von Neumann regular rings.

• 대한수학회지
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• 제54권5호
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• pp.1505-1519
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• 2017

Assume that M is an R-module where R is a commutative ring. A proper submodule N of M is called a weakly 2-absorbing primary submodule of M if $0{\neq}abm{\in}N$ for any $a,b{\in}R$ and $m{\in}M$, then $ab{\in}(N:M)$ or $am{\in}M-rad(N)$ or $bm{\in}M-rad(N)$. In this paper, we extended the concept of weakly 2-absorbing primary ideals of commutative rings to weakly 2-absorbing primary submodules of modules. Among many results, we show that if N is a weakly 2-absorbing primary submodule of M and it satisfies certain condition $0{\neq}I_1I_2K{\subseteq}N$ for some ideals $I_1$, $I_2$ of R and submodule K of M, then $I_1I_2{\subseteq}(N:M)$ or $I_1K{\subseteq}M-rad(N)$ or $I_2K{\subseteq}M-rad(N)$.

• 호남수학학술지
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• 제31권3호
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• pp.429-436
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• 2009

In this short paper, we prove some new properties on homogeneous ideals and primary ideals of R(+)M.

• 대한수학회논문집
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• 제34권3호
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• pp.729-741
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• 2019

In this paper we give a full characterization of prime submodules of a finitely generated projective module M over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module M and study submodules of M which satisfy the radical formula.

• 호남수학학술지
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• 제27권3호
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• pp.343-351
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• 2005

The notion of expansions of filters in $R_0$-algebras is introduced. Also the notion of ${\sigma}$-primary filters in $R_0$-algebras is discussed.