ABSOLUTE IRREDUCIBILITY OF BIVARIATE POLYNOMIALS VIA POLYTOPE METHOD

Abstract

For any field F, a polynomial f is an element of F[x(1), x(2),., x(k)] 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 results giving new integrally indecomposable classes of polygons. Consequently, we have some criteria giving many types of absolutely irreducible bivariate polynomials over arbitrary fields.