Tropical Ideals

Abstract

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

Keywords

• [math.math-co]mathematics [math]/combinatorics [math.co]