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Irreducibility of polynomials and diophantine equations

Title
Irreducibility of polynomials and diophantine equations
Authors
Woo S.S.
Ewha Authors
우성식
SCOPUS Author ID
우성식scopus
Issue Date
2010
Journal Title
Journal of the Korean Mathematical Society
ISSN
0304-9914JCR Link
Citation
vol. 47, no. 1, pp. 101 - 112
Indexed
SCIE; SCOPUS; KCI WOS scopus
Abstract
In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. In this paper, we consider the polynomials with coefficients in a field and divisibility of a polynomial by a polynomial with a certain degree is equivalent to the existence of common solution to a system of Diophantine equations. As an application we construct a family of irreducible quartics over Q which are not of Eisenstein type. © 2010 The Korean Mathematical Society.
DOI
10.4134/JKMS.2010.47.1.101
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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