Integral polytopes and polynomial factorization.

For any field F, there is a relation between the factorization of a polynomial f ∈ F[x₁, ..., x_n] and the integral decomposition of the Newton polytope of f. We extended this result to polynomial rings R[x₁, ..., x_n] where R is any ring containing some elements which are not zero-divisors. Moreover, we have constructed some new families of integrally indecomposable polytopes in ℝⁿ giving infinite families of absolutely irreducible multivariate polynomials over arbitrary fields. [ABSTRACT FROM AUTHOR]