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.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/3/12604873/index.pdf |
| Date | 01 April 2004 |
| Creators | Koyuncu, Fatih |
| Contributors | Ozbudak, Ferruh |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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