This analysis investigates prime ideals' structures in tropical polynomial semirings, suggesting implications for algebraic geometry.
In this paper 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”.
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Joó et al. (2026) studied this question.
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