Supertropical polynomials and resultants

Zur Izhakian, Louis Rowen

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


This paper, a continuation of Izhakian and Rowen (in press) [5], involves a closer study of polynomials over supertropical semirings and their version of tropical geometry. We introduce the concept of relatively prime polynomials (in one indeterminate) and resultants, with the aid of some topology. Polynomials in one indeterminant are seen to be relatively prime iff they do not have a common tangible root, iff their resultant is tangible. Applying various morphisms of supertropical varieties leads to a supertropical version of Bézout's theorem.

Original languageEnglish
Pages (from-to)1860-1886
Number of pages27
JournalJournal of Algebra
Issue number8
StatePublished - Oct 2010
Externally publishedYes


  • Bézout's theorem
  • Matrix algebra
  • Relatively prime
  • Resultant
  • Supertropical algebra
  • Supertropical polynomials


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