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Idempotence of finitely generated commutative semifields (1910.02457v1)
Published 6 Oct 2019 in math.AC and math.RA
Abstract: We prove that a commutative parasemifield S is additively idempotent provided that it is finitely generated as a semiring. Consequently, every proper commutative semifield T that is finitely generated as a semiring is either additively constant or additively idempotent. As part of the proof, we use the classification of finitely generated lattice-ordered groups to prove that a certain monoid associated to the parasemifield S has a distinguished geometrical property called prismality.