Dergiler / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 1
Integral polytopes and polynomial factorization
- Sayfa
- 18–26
- DOI
- —
Özet
For any field F, there is a relation between the factorization of a polynomial f \in F[x1,...,xn] and the integral decomposition of the Newton polytope of f. We extended this result to polynomial rings R[x1,...,xn] 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.
Abstract
For any field F, there is a relation between the factorization of a polynomial f \in F[x1,...,xn] and the integral decomposition of the Newton polytope of f. We extended this result to polynomial rings R[x1,...,xn] 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.