Irreducible polynomials by the polytope method over integral domains

Abstract

Ostrowski realized that there is a relation between the factorization of a multivariate polynomial over any field and the integral decomposition of the Newton polytope of this polynomial. Here, we extended this result to the multivariate polynomials over any integral domain. Moreover, we observed that this result is also valid for some special kind of multivariate polynomials over any commutative ring.