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arXiv · 1910.02457

Idempotence of finitely generated commutative semifields

Vítězslav Kala·Miroslav Korbelář
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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.

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Vítězslav Kala, Miroslav Korbelář. 2019-10-06. Idempotence of finitely generated commutative semifields. https://doi.org/10.1515/forum-2017-0098

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