Varieties of prime tropical ideals and the dimension of the coordinate semiring
arXiv:2501.18053
Abstract
In this note we study the relationship between ideals and congruences of the tropical polynomial and Laurent polynomial semirings. We show that the variety of a non-zero prime ideal of the tropical (Laurent) polynomial semiring consists of at most one point. We also prove a result relating the dimension of an affine tropical variety and the dimension of its coordinate semiring.
16 pages; small corrections in this version. Comments welcome!