Semifields and a theorem of Abhyankar

Abstract

Abstract. Abhyankar [1] 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 , . . . , Tn] (for some n depending on the field). We conjecture that his result can not 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 [2], [7].