Ideals of polynomial semirings in tropical mathematics

Zur Izhakian, Louis Rowen

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3 Scopus citations


We describe the ideals, especially the prime ideals, of semirings of polynomials over layered domains, and in particular over supertropical domains. Since there are so many of them, special attention is paid to the ideals arising from layered varieties, for which we prove that every prime ideal is a consequence of finitely many binomials. We also obtain layered tropical versions of the classical Principal Ideal Theorem and Hilbert Basis Theorem.

Original languageEnglish
Article number1250143
JournalJournal of Algebra and its Applications
Issue number2
StatePublished - Mar 2013
Externally publishedYes


  • Hilbert Basis Theorem
  • Noetherian ideal theory
  • Principal Ideal Theorem
  • Tropical and supertropical algebra
  • layered algebra
  • layered ideals


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