Integral polytopes and polynomial factorization

Koyuncu F.

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

  • Publication Type: Article / Article
  • Volume: 37 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1009-17
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.18-26
  • Ankara Yıldırım Beyazıt University Affiliated: No

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.