Congruences and coordinate semirings of tropical varieties

Zur Izhakian*, Louis Rowen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this paper we present two intrinsic algebraic definitions of tropical variety motivated by the classical Zariski correspondence. Our main definition applies Zariski density to the algebraic structure of the coordinate semiring of an affine supertropical algebraic set, which we tie to tropical geometry, especially in connection with the dimension of an affine variety, obtaining the analogs of classical results from dimension theory including catenarity. The second approach, based on the layered structure, is given in the appendix.

Original languageEnglish
Pages (from-to)231-259
Number of pages29
JournalBulletin des Sciences Mathematiques
Issue number3
Early online date29 Dec 2015
Publication statusPublished - Apr 2016


  • Admissible variety
  • Catenarity
  • Coordinate semiring
  • Dimension
  • Primary
  • Secondary
  • Supertropical algebra
  • Tropical geometry


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