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ANNIHILATORS IN ONE-SIDED IDEALS GENERATED BY COEFFICIENTS OF ZERO-DIVIDING POLYNOMIALS
곽태근,이동수,이양 대한수학회 2014 대한수학회지 Vol.51 No.3
Nielsen and Rege-Chhawchharia called a ring R right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, there exists a nonzero element r ∈ R with f(x)r = 0. Hong et al. called a ring R strongly right McCoy if given nonzero polynomials f(x),g(x) over R with f(x)g(x) = 0, f(x)r = 0 for some nonzero r in the right ideal of R generated by the coefficients of g(x). Subsequently, Kim et al. observed similar conditions on linear polynomials by finding nonzero r’s in various kinds of one-sided ideals generated by coefficients. But almost all results obtained by Kim et al. are concerned with the case of products of linear polynomials. In this paper we examine the nonzero annihilators in the products of general polynomials.
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Reflexive property on idempotents
곽태근,이양 대한수학회 2013 대한수학회보 Vol.50 No.6
The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. In this note we study the structure of idempotents satisfying the reflexive property and introduce reflexive-idempotents-property (simply, RIP) as a generalization.It is proved that the RIP can go up to polynomial rings, power series rings, and Dorroh extensions. The structure of non-Abelian RIP rings of minimal order (with or without identity) is completely investigated.
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루브릭(rubric)을 활용한 관찰평가 도구의 적용 경험
곽태근,조한무 한국홀리스틱융합교육학회 2012 홀리스틱융합교육연구 Vol.16 No.3
이 연구의 목적은 루브릭을 활용한 관찰평가 도구의 적용 사례 경험을 이해하는 데 있다. 연구대상은 경기도 화성시 A초등학교에서 15명 대상으로 설문지를 통하여 조사한 결과 연구목적에 적합한 교사 8명을 선정하여 면담을 실시하였으며, 이들 중에 연구에 의미가 있는 교사 3명을 최종 선정하였다. 루브릭을 활용한 관찰평가 도구를 구안하고, 이에 대한 타당성 확보와 연구 목적의 적합성을 점검하기 위해서 3차례의 예비연구를 실시하였으며 예비연구를 통해 완성된 루브릭을 활용한 관찰 평가 도구를 6차시 배드민턴 수업에 적용하여, 심층면담, 비디오 촬영, 수업의 서술적 관찰, 관련 문서자료를 통해 자료를 수집하였다. 수집된 자료는 사례 기록 분석, 귀납적 범주 분석을 통해 분석하였으며 평가의 실효성, 교육적 효과, 교사의 전문성으로 범주화하였다. 평가의 실용성은 경제적 평가, 생활통지표 활용의 최적 도구, 교육 관련자에게 주는 이로움의 주제로 분류하였고, 교육적 효과는 피드백 제공의 용이, 자율적 참여, 경기력 향상의 주제로 분류하였다. 교사의 전문성은 도구 제작 쉬움, 도구 제작 어려움, 빠르게 학생수준 파악의 주제로 분류하였다. The purpose of this study was observed using the rubric assessment tools look at the examples are viewing. Suitable for research purposes, to 8 teachers, the interview was selected during the study, Hwaseong-si, Gyeonggi-A Elementary School to 15 students through questionnaire survey meaning that teachers in the study, 3 patients finalist. Development and observation rubric assessment tool, in order to check the suitability of the validity of security and research purposes for observation assessment tool completed the preliminary research through the rubrics, a preliminary study was conducted three rounds of six class apply the lessons to badminton, data were collected through in-depth interviews, shooting video, descriptive observation of lessons, and related documentation. Recorded on a case-by-case analysis of the collected data were analyzed through inductive category analysis, evaluation of effectiveness, educational effectiveness, and were categorized by the professionalism of teachers. Educational effectiveness evaluation of the practicality of the economic evaluation, the optimal tool life, take advantage of report cards, and that the benefits of education to a group of people, subjects were classified as easy to provide feedback to the subject of the voluntary participation, performance-enhancing classification. Professionalism of teachers authoring tool easy tool production difficulties, quickly to identify the subject of the student level were classified.
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On commutativity of regular products
곽태근,이양,서연숙 대한수학회 2018 대한수학회보 Vol.55 No.6
We study the one-sided regularity of matrices in upper triangular matrix rings in relation with the structure of diagonal entries. We next consider a ring theoretic condition that $ab$ being regular implies $ba$ being also regular for elements $a, b$ in a given ring. Rings with such a condition are said to be {\it commutative at regular product} (simply, {\it CRP} rings). CRP rings are shown to be contained in the class of directly finite rings, and we prove that if $R$ is a directly finite ring that satisfies the descending chain condition for principal right ideals or principal left ideals, then $R$ is CRP. We obtain in particular that the upper triangular matrix rings over commutative rings are CRP.
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Extensions of extended symmetric rings
곽태근 대한수학회 2007 대한수학회보 Vol.44 No.4
An endomorphism of a ring R is called right (left) symmet-ric if whenever abc = 0 for a;b;c2 R,ac (b) = 0 ((b)ac = 0). A ring Ris called right (left) -symmetricif there exists a right (left) symmetricendomorphism of R. The notion of an -symmetric ring is a general-ization of -rigid rings as well as an extension of symmetric rings. Westudy characterizations of-symmetric rings and their related propertiesincluding extensions. The relationship between -symmetric rings and(extended) Armendariz rings is also investigated, consequently severalknown results relating to -rigid and symmetric rings can be obtained ascorollaries of our results.
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On Jacobson and nil radicals related to polynomial rings
곽태근,이양,A. Cigdem Ozcan 대한수학회 2016 대한수학회지 Vol.53 No.2
This note is concerned with examining nilradicals and Jacobson radicals of polynomial rings when related factor rings are Armendariz. Especially we elaborate upon a well-known structural property of Armendariz rings, bringing into focus the Armendariz property of factor rings by Jacobson radicals. We show that $J(R[x])=J(R)[x]$ if and only if $J(R)$ is nil when a given ring $R$ is Armendariz, where $J(A)$ means the Jacobson radical of a ring $A$. A ring will be called {\it feckly Armendariz} if the factor ring by the Jacobson radical is an Armendariz ring. It is shown that the polynomial ring over an Armendariz ring is feckly Armendariz, in spite of Armendariz rings being not feckly Armendariz in general. It is also shown that the feckly Armendariz property does not go up to polynomial rings.
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곽태근,이양 대한수학회 2016 대한수학회보 Vol.53 No.6
CORRIGENDUM TO “REFLEXIVE PROPERTY ON IDEMPOTENTS” [BULL. KOREAN MATH. SOC. 50 (2013), NO. 6, 1957–1972]
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On generalizations of δ-rigid rings
Kwak, Tai Keun,Yoon, Haeng Won 대진대학교 1998 大眞論叢 Vol.6 No.-
본 논문은 σr-rigid 환R의 한 일반화로서 다음의 조건 (*)를 만족하는 endomorphism σ의 특성들을 2-primal 환 위에서 연구한다. 조건(*): α∈R에 대하여, ασ(α)∈ P(R)이면 α∈ P(R)이다. 여기서 P(R)은 환R의 prime radical을 나타낸다. 이때, 조건 (*)을 만족하는 환을 σ(*) -환이라고 부른다.
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CONGRUENCE EXTENSION PROPERTY IN SEMIGROUPS
Kwak, Tai Keun,Park, Young Seo 대진대학교 1994 大眞論叢 Vol.2 No.-
반군이 합동식 확대성을 갖는다는 것은 각각의 부분 반군위에서 합동식이 반군에 확대될수있음을 말한다. 이 논문에서는 이데알 확대성과 군 합동식 확대성에 기인해서 그 성질을 연구하였다.
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ON THE PRIME SPECTRUM OF 2-PRIMAL RINGS(Ⅱ)
Kwak, Tai Keun 대진대학교 1996 大眞論叢 Vol.4 No.-
본 논문은 환 R이 2-프라이말 일 때, R의 모든 소(素) 이태알이 극대(極大) 이데알일 필요충분조건은 R의 스펙트럼 공간이 정규(正規) T₂-공간임을 보였으며, Gelfand 준동형사상이 동형사상이 되지않는 예를 제시하였다.
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