• 한국수학교육학회지시리즈A:수학교육
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• 제48권1호
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• pp.81-91
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• 2009

This paper focuses on two problems in the 10th grade mathematics, the rational zero theorem and the content(the integer divisor) of a polynomial Among 138 students participated in the problem solving, 58 of them (42 %) has used the rational zero theorem for the factorization of polynomials. However, 30 of 58 students (52 %) consider the rational zero theorem is a mathematical fake(false statement) and they only use it to get a correct answer. There are three different types in the textbooks in dealing with the content of a polynomial with integer coefficients. Computing the greatest common divisor of polynomials, some textbooks consider the content of polynomials, some do not and others suggest both methods. This also makes students confused. We suggests that a separate section of the rational zero theorem must be included in the text. As for the content of a polynomial, we consider the polynomials are contained in the polynomial ring over the rational numbers. So computing the gcd of polynomials, guide the students to give a monic(or primitive) polynomial as ail answer.

• 대한수학회보
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• 제54권5호
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• pp.1757-1771
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• 2017

Let K be a field and G be a group of its automorphisms. It follows from Speiser's generalization of Hilbert's Theorem 90, [10] that any K-semilinear representation of the group G is isomorphic to a direct sum of copies of K, if G is finite. In this note three examples of pairs (K, G) are presented such that certain irreducible K-semilinear representations of G admit a simple description: (i) with precompact G, (ii) K is a field of rational functions and G permutes the variables, (iii) K is a universal domain over field of characteristic zero and G its automorphism group. The example (iii) is new and it generalizes the principal result of [7].

• KDI Journal of Economic Policy
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• 제12권1호
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• pp.127-148
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• 1990

이 논문의 기본목표는 Bain 이래 논란의 대상이 되어 온 기존기업들에 의한 진입제한가격(進入制限價格)의 형성이 일반적으로 가능한가, 가능하다면 어떠한 메커니즘을 통해 형성되는 가를 밝히고, 진입제한가격이론(進入制限價格理論)이 한국경제에 갖는 의의를 찾아보는데 있다, 이 논문에서 밝혀질 주요결과는 다음과 같다. 첫째, 다수의 기존기업(旣存企業)이 각자의 이윤극대화(利潤極大化)를 추구하며 카르텔을 형성하지 않는 때에도 기존기업(旣存企業)과 잠재적(潛在的) 신규기업간(新規企業間)에 정보의 불균형이 존재하는 경우 진입제한가격(進入制限價格)이 채택될 가능성이 있다. 둘째, 이러한 과점기업(寡占企業)들에 의한 진입제한가격형성(進入制限價格形成)은 암묵적 담합의 새로운 형태로 해석할 수 있다. 셋째, 진입제한가격형성(進入制限價格形成)은 각종 회계자료(會計資料)가 공표되지 않을 경우에 가능하다. 넷째, 기존기업(旣存企業)의 수(數)가 증가하여 산업(産業)이 완전경쟁산업(完全競爭産業)에 접근해 감에 따라 진입제한가격(進入制限價格)이 형성될 가능성은 사라지게 된다.