• 대한수학회보
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• 제58권4호
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• pp.865-876
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• 2021

Let 𝔽 be a commutative ring. A restricted skew polynomial extension over 𝔽 is a class of iterated skew polynomial 𝔽-algebras which include well-known quantized algebras such as the quantum algebra U_q(𝔰𝔩₂), Weyl algebra, etc. Here we obtain a necessary and sufficient condition in order to be restricted skew polynomial extensions over 𝔽. We also introduce a restricted Poisson polynomial extension which is a class of iterated Poisson polynomial algebras and observe that a restricted Poisson polynomial extension appears as semiclassical limits of restricted skew polynomial extensions. Moreover, we obtain usual as well as unusual quantized algebras of the same Poisson algebra as applications.

• 충청수학회지
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• 제22권3호
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• pp.497-506
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• 2009

This work studies about the composition polynomial f(g(x)) that preserves certain properties of f(x) and g(x). We shall investigate necessary and sufficient conditions of f(x) and g(x) to be f(g(x)) is separable, solvable by radical or split completely. And we find relationship of Galois groups of f(g(x)), f(x) and of g(x).

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.41-60
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• 2000

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author's work. concerning parameter identification of linear dynamic stochastic system. Special attention is given of searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.

• 대한수학회논문집
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• 제22권2호
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• pp.183-194
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• 2007

For an irreducible binomial polynomial $f(x)=x^n-b{\in}K[x]$ with a field K, we ask when does the mth iteration $f_m$ is irreducible but $m+1th\;f_{m+1}$ is reducible over K. Let S(n, m) be the set of b's such that $f_m$ is irreducible but $f_{m+1}$ is reducible over K. We investigate the set S(n, m) by taking K as the rational number field.

• 호남수학학술지
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• 제33권3호
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• pp.355-366
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• 2011

In this paper we investigate criteria that for an irreducible monic quadratic polynomial f(x) ${\in}$ $\mathbb{Q}$[x], $f{\circ}g$ is reducible over $\mathbb{Q}$ for an irreducible polynomial g(x) ${\in}$ $\mathbb{Q}$[x]. Odoni intrigued the discussion about an explicit form of irreducible polynomials f(x) such that $f{\cric}f$ is reducible. We construct a system of infitely many such polynomials.

• 충청수학회지
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• 제24권4호
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• pp.713-724
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• 2011

We investigate the irreducibility of iterate and composite polynomials. For this purpose discriminant and resultant are computed by means of the norm function.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권3호
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• pp.283-296
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• 2009

Let f(x) = $x^n\;+\;a$ be a binomial polynomial in Z[x] and $f_m(x)$ be the m-th iterate of f(x). In this work we study a necessary condition to be the Galois group of $f_m(x)$ is isomorphic to a wreath product group $[C_n]^m$ where $C_n$ is a cyclic group of order n.

• 대한수학회논문집
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• 제13권3호
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• pp.461-464
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• 1998

We generalize the Artin-Rees Theorem about the AR-property and study linking diagram in the set of prime ideals of the coordinate ring of quantum affine space.

• 호남수학학술지
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• 제32권3호
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• pp.493-514
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• 2010

The resultant and discriminant of composite polynomials were studied by McKay and Wang using some algebraic properties. In this paper we study the resultant and discriminant of iterate polynomials. We shall use elementary computations of matrices and block matrix determinants; this could provide not only the values but also the visual structure of resultant and discriminant from elementary matrix calculation.