Geodesic
Semifields and a theorem of Abhyankar
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 267-273.

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Abhyankar proved that every field of finite transcendence degree over $\mathbb{Q}$ or over a finite field is a homomorphic image of a subring of the ring of polynomials $\mathbb{Z}[T_1,\dots, T_n]$ (for some $n$ depending on the field). We conjecture that his result cannot be substantially strengthened and show that our conjecture implies a well-known conjecture on the additive idempotence of semifields that are finitely generated as semirings.
DOI : 10.14712/1213-7243.2015.216
Classification : 12K10, 13B25, 16Y60
Keywords: Abhyankar's construction; semiring; semifield; finitely generated; additively idempotent 
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Kala, Vítězslav. Semifields and a theorem of Abhyankar. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 267-273. doi : 10.14712/1213-7243.2015.216. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.216/

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