Integral polytopes and polynomial factorization


Koyuncu F.

Turkish Journal of Mathematics, vol.37, no.1, pp.18-26, 2013 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1009-17
  • Title of Journal : Turkish Journal of Mathematics
  • Page Numbers: pp.18-26

Abstract

For any field F, there is a relation between the factorization of a polynomial f is an element of 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 R-n giving infinite families of absolutely irreducible multivariate polynomials over arbitrary fields.