Integral polytopes and polynomial factorization

Authors : Fatih KOYUNCU

Pages : 18-26

Doi:10.3906/mat-1009-17

View : 9 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

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.
Keywords : Key words Integral polytopes, integral indecomposability, multivariate polynomials, absolute irreducibility