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Varieties of prime tropical ideals and the dimension of the coordinate semiring (2501.18053v1)
Published 29 Jan 2025 in math.AG and math.AC
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.