Galois extensions and O*-fields

被引：0

作者：

Evans, Kenneth ^{[1
]}

Ma, Jingjing ^{[1
]}

机构：

[1] Univ Houston Clear Lake, Dept Math, 2700 Bay Area Blvd, Houston, TX 77058 USA

来源：

POSITIVITY | 2023年 / 27卷 / 02期

基金：

美国国家科学基金会;

关键词：

Galois extension; Infinite prime; O*-field; Normal closure; Number field; Archimedean maximal partial order;

D O I：

10.1007/s11117-023-00982-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A field F is O* if each partial order that makes F a partially ordered field can be extended to a total order that makes F a totally ordered field. We use the theory of infinite primes developed by Dubois and Harrison to prove the following. For a subfield F of C that is finite-dimensional over Q, we prove that when F is Galois over Q, F is an O*-field if and only if is a subfield of R. We find other conditions that make F an O*-field and provide several examples. As well for an arbitrary field of characteristic 0, we characterize the maximal partial orders that are Archimedean.

引用

页数：13

共 50 条

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