Prime congruences containing a bend congruence on toric semirings are strongly characterized, yielding a Nullstellensatz analogue, cancellativity of certain quotients, identification with tropical function semirings, and polyhedron closure descriptions.
Song,T-algebra homomorphisms between rational function semifields of tropical curvesarxiv preprint ArXiv:2304.03508 (2023)
2 Pith papers cite this work. Polarity classification is still indexing.
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Defines abstract tropical curves with parallel rays and proves a contravariant categorical equivalence between their category and the category of T-semifields with algebra homomorphisms.
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Geometric classification of primes modulo a (bend) congruence
Prime congruences containing a bend congruence on toric semirings are strongly characterized, yielding a Nullstellensatz analogue, cancellativity of certain quotients, identification with tropical function semirings, and polyhedron closure descriptions.
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Tropical curves with parallel rays
Defines abstract tropical curves with parallel rays and proves a contravariant categorical equivalence between their category and the category of T-semifields with algebra homomorphisms.