Semifields and a theorem of Abhyankar

[摘要] 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.

[学科分类] 物理化学和理论化学

[关键词] Abhyankar\'s construction;semiring;semifield;finitely generated;additively idempotentDOI: DOI 10.14712/1213-7243.2015.216AMS Subject Classification: 12K10 13B25 16Y60 PDF