Semifields and a theorem of Abhyankar

Commentationes mathematicae Universitatis Carolinae

V\xc3\xadt\xc4\x9bzslav Kala

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;   

DOI  :  10.14712/1213-7243.2015.216

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 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.

【 授权许可】

CC BY