Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Tropical Ideals
Diane Maclagan  1  , Felipe Rincon  2  
1 : Warwick Mathematics Institute  (WMI)  -  Website
Mathematics Institute, Zeeman Building, The University of Warwick, Coventry CV4 7AL, United Kingdom -  Royaume-Uni
2 : Department of Mathematics, University of Oslo

We introduce and study a special class of ideals over the semiring of tropical polynomials, which we call
tropical ideals, with the goal of developing a useful and solid algebraic foundation for tropical geometry. We explore
their rich combinatorial structure, and prove that they satisfy numerous properties analogous to classical ideals.

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