Ayrışamayan integral politoplar ve mutlak indirgenemez çok değişkenli polinomlar

Abstract

In this thesis, absolute irreducibility of multivarite polynomials over any field F,with the help of Newton polytopes of these polynomials, is studied.For any field F, a polynomial f 2 F[x1, x2, ..., xn] can be associated to a Newtonpolytop. If f has an integrally indecomposable Newton polytope, with respect tominkowski sum, then f is absolutely irreducible over F, i.e. it is irreducible over anyalgebraic extension of F.In this study, considering some integrally indecomposable Newton polytopes,some families of absolutely irreducible multivarite polynomials associated to thesepolytopes are given.Key Words : Multivarite polynomials, absolute irreducibility, integrally inde-composable Newton polytopes.