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Factorization over local fields and the irreducibility of generalized difference polynomials

Part of: General field theory

Published online by Cambridge University Press:  26 February 2010

S. D. Cohen ,
A. Movahhedi  and
A. Salinier
S. D. Cohen
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland.
A. Movahhedi
Affiliation:
UPRES A 6090 CNRS, Faculté des Sciences, 123 Avenue Albert Thomas, 87060 Limoges Cedex, France.
A. Salinier
Affiliation:
UPRES A 6090 CNRS, Faculté des Sciences, 123 Avenue Albert Thomas, 87060 Limoges Cedex, France.
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Extract

Let E be a local field, i.e., a field which is complete with respect to a rank one discrete valuation υ (we do not require any finiteness condition on the residue class field of E). Let f(X) be a polynomial in one variable, with coefficients in E. It is well known [4, 6, 9, 11, 13] that the Newton polygon method allows us to gather information about the factorization of f(X). This method consists of attaching to each side S of a Newton polygon of f(X) a factor (not necessarily irreducible) of f(X), the degree of which is the length of the horizontal projection of S.

MSC classification

Secondary: 12E05: Polynomials (irreducibility, etc.)

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Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 173 - 196
Copyright
Copyright © University College London 2000

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