Semifields and a theorem of Abhyankar. (English) Zbl 1434.12009

Summary: S. S. Abhyankar [Proc. Am. Math. Soc. 139, No. 9, 3067–3082 (2011; Zbl 1227.14004)] 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.


12K10 Semifields
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13B25 Polynomials over commutative rings
16Y60 Semirings


Zbl 1227.14004
Full Text: DOI arXiv


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