The Artin-Schreier Theorem in Galois Theory 公开

Abstract

We first list and state some basic definitions and theorems of the Galois theory of finite extensions, as well as state and prove the Kummer theory and the Artin-Schreier extensions as prerequisites. The main part of this thesis is the proof of the Artin-Schreier Theorem, which states that an algebraic closed field having finite extension with its subfield F has degree at most two and F must have characteristic 0. After the proof, we will discuss the applications for the Artin-Schreier Theorem.

Table of Contents

Contents

1 Introduction 1

2 Basic Definitions, Theorems, And Some Lemmas 2

1. 2.1 Field Theory ................................ 2
2. 2.2 Galois Theory................................ 11

3 The Artin-Schreier Extension 21

4 Kummer Theory 26

5 The Artin-Schreier Theorem 28

6 Applications 33

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	BS
Submission	Honors Thesis
Language	English
Research Field	Mathematics
关键词	Artin-Schreier Galois
Committee Chair / Thesis Advisor	Venapally, Suresh , Emory University
Committee Members	Raman, Parimala, Emory University Liu, Ruixuan , Emory University

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