Integral polytopes and polynomial factorization

For any field F, there is a relation between the factorization of a polynomial f in F[x_1,...,x_n] and the integral decomposition of the Newton polytope of f. We extended this result to polynomial rings R[x_1,...,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 mb giving infinite families of absolutely irreducible multivariate polynomials over arbitrary fields.