Embedded Picard-Vessiot extensions

被引：4

作者：

Brouette, Quentin ^{[1
]}

Cousins, Greg ^{[2
]}

Pillay, Anand ^{[2
]}

Point, Francoise ^{[3
]}

机构：

[1] Univ Mons, Math, Mons, Belgium

[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[3] UMH, FRS FNRS, Mons, Belgium

来源：

COMMUNICATIONS IN ALGEBRA | 2018年 / 46卷 / 11期

基金：

美国国家科学基金会;

关键词：

Almost quantifier elimination; bounded field; differential field; large field; Picard-Vessiot; FIELDS;

D O I：

10.1080/00927872.2018.1448848

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if T is a theory of large, bounded, fields of characteristic 0 with almost quantifier elimination, and T-D is the model companion of T{ is a derivation}, then for any model (?,) of T-D, differential subfield K of ? such that C-K?T, and linear differential equation Y=AY over K, there is a Picard-Vessiot extension L of K for the equation with KL?, i.e. L can be embedded in ? over K, as a differential field. Moreover such L is unique to isomorphism over K as a differential field. Likewise for the analogue for strongly normal extensions for logarithmic differential equations in the sense of Kolchin.

引用

页码：4609 / 4615

页数：7

共 15 条

[1]

Brouette Q., MATH LOG Q

[2] Real and p-adic Picard-Vessiot fields [J].