Journal of the
Korean Mathematical Society JKMS

For any field $F,$ a polynomial $f\in F[x_1,x_2,\ldots,x_k]$ 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.

Keywords: absolute irreducibility, bivariate polynomials, integral polygons, integral indecomposability, polytope method

MSC numbers: 51E12, 52B12