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A Geometric Approach To Absolute Irreducibility Of Polynomials

This thesis is a contribution to determine the absolute irreducibility of
polynomials via their Newton polytopes.
For any field F / a polynomial f in F[x1, x2,..., xk] can be associated with
a polytope, called its Newton polytope. If the polynomial f has integrally
indecomposable Newton polytope, in the sense of Minkowski sum, then it is
absolutely irreducible over F / i.e. irreducible over every algebraic extension
of F. We present some new results giving integrally indecomposable classes
of polytopes. Consequently, we have some new criteria giving infinitely many
types of absolutely irreducible polynomials over arbitrary fields.

Identiferoai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/3/12604873/index.pdf
Date01 April 2004
CreatorsKoyuncu, Fatih
ContributorsOzbudak, Ferruh
PublisherMETU
Source SetsMiddle East Technical Univ.
LanguageEnglish
Detected LanguageEnglish
TypePh.D. Thesis
Formattext/pdf
RightsTo liberate the content for public access

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