Abstract
Abhyankar proved that every field of finite transcendence degree over Q or over a finite field is a homomorphic image of a subring of the ring of polynomials Z[T-1,..., 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.