Integral polytopes and polynomial factorization


Koyuncu F.

Turkish Journal of Mathematics, cilt.37, ss.18-26, 2013 (SCI Expanded İndekslerine Giren Dergi) identifier

  • Cilt numarası: 37 Konu: 1
  • Basım Tarihi: 2013
  • Doi Numarası: 10.3906/mat-1009-17
  • Dergi Adı: Turkish Journal of Mathematics
  • Sayfa Sayıları: ss.18-26

Özet

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.