## Notre Dame Mathematical Lectures

- Galois Theory
- 1971, 21-68

### Chapter II: Field Theory

#### Abstract

Contents

- A. Extension Fields
- B. Polynomials
- C. Algebraic Elements
- D. Splitting Fields
- E. Unique Decomposition of Polynomials into Irreducible Factors
- F. Group Characters
- G. Applications and Examples to Theorem 13
- H. Normal Extensions
- I. Finite Fields
- J. Roots of Unity
- K. Noether Equations
- L. Kummer's Fields
- M. Simple Extensions
- N. Existence of a Normal Basis
- O. Theorem of Natural Rationality

#### Chapter information

**Source***Galois Theory: Lectures Delivered at the University of Notre Dame*, ed. and suppl. with a section on applications by Dr. Arthur N. Milgram, 2nd ed. (Notre Dame, Ind.: University of Notre Dame, 1971)

**Dates**

First available in Project Euclid: 29 March 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.ndml/1175197045

**Rights**

Copyright © 1971, University of Notre Dame

#### Citation

Artin, Emil. Chapter II: Field Theory. Galois Theory, 21--68, University of Notre Dame, Notre Dame, Indiana, 1971. https://projecteuclid.org/euclid.ndml/1175197045.