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.
Funding statement: The first author was supported by Neuron Impulse award and by Charles University Research Centre program UNCE/SCI/022.
Acknowledgements
We wish to thank the anonymous referee for a careful reading of the manusript and for several comments and suggestions that have helped improve the article.
References
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