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A geometric approach to absolute irreducibility of polynomials

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2004
Koyuncu, Fatih
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.