Semifields and a theorem of Abhyankar

Vítězslav Kala

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 3, page 267-273
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kala, Vítězslav. "Semifields and a theorem of Abhyankar." Commentationes Mathematicae Universitatis Carolinae 58.3 (2017): 267-273. <http://eudml.org/doc/294111>.

@article{Kala2017,
abstract = {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.},
author = {Kala, Vítězslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Abhyankar's construction; semiring; semifield; finitely generated; additively idempotent},
language = {eng},
number = {3},
pages = {267-273},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Semifields and a theorem of Abhyankar},
url = {http://eudml.org/doc/294111},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Kala, Vítězslav
TI - Semifields and a theorem of Abhyankar
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 3
SP - 267
EP - 273
AB - 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.
LA - eng
KW - Abhyankar's construction; semiring; semifield; finitely generated; additively idempotent
UR - http://eudml.org/doc/294111
ER -

References

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