Layered tropical mathematics

Zur Izhakian, Manfred Knebusch, Louis Rowen

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


Generalizing supertropical algebras, we present a “layered” structure, “sorted” by a semiring which permits varying ghost layers, and indicate how it is more amenable than the “standard” supertropical construction in factorizations of polynomials, description of varieties, and for mathematical analysis and calculus, in particular with respect to multiple roots of polynomials. This gives rise to a significantly better understanding of the tropical resultant and discriminant. Explicit examples and comparisons are given for various sorting semirings such as the natural numbers and the positive rational numbers, and we see how this theory relates to some recent developments in the tropical literature.
Original languageEnglish
Pages (from-to)200-273
Number of pages74
JournalJournal of Algebra
Early online date11 Jul 2014
Publication statusPublished - 15 Oct 2014

Bibliographical note

The research of the first and third authors was supported by the Israel Science Foundation (grant No. 448/09).

The research of the first author also was conducted under the auspices of the Oberwolfach Leibniz Fellows Programme (OWLF), Mathematisches Forschungsinstitut Oberwolfach, Germany.

This research of the second author was supported in part by the Gelbart Institute at Bar-Ilan University, the Minerva Foundation at Tel-Aviv University, the Department of Mathematics of Bar-Ilan University, the Emmy Noether Institute at Bar-Ilan University, and the Mathematisches Forschungsinstitut Oberwolfach.


  • Tropical algebra
  • Layered supertropical domains
  • Polynomial semiring
  • Resultant
  • Sylvester matrix
  • Discriminant
  • Layered derivatives


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