**Courant Lecture Notes**

Volume: 15;
2007;
126 pp;
Softcover

MSC: Primary 12;

Print ISBN: 978-0-8218-4129-7

Product Code: CLN/15

List Price: $32.00

Individual Member Price: $25.60

**Electronic ISBN: 978-1-4704-3115-0
Product Code: CLN/15.E**

List Price: $32.00

Individual Member Price: $25.60

# Algebra with Galois Theory

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*Emil Artin*

Notes by Albert A. Blank

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

The present text was first published in 1947 by the Courant Institute of Mathematical Sciences of New York University. Published under the title Modern Higher Algebra. Galois Theory, it was based on lectures by Emil Artin and written by Albert A. Blank. This volume became one of the most popular in the series of lecture notes published by Courant. Many instructors used the book as a textbook, and it was popular among students as a supplementary text as well as a primary textbook. Because of its popularity, Courant has republished the volume under the new title Algebra with Galois Theory.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

#### Readership

Undergraduate students interested in algebra.

#### Reviews & Endorsements

Artin's book is a gem...one of the most elegantly presented texts on Galois theory... In summary, this book is a valuable supplement for a course on Galois theory.

-- Mathematical Reviews

It is still amazing to see how elegantly, masterly and comprehensibly Emil Artin taught such a topic like Galois theory sixty years ago. Using the modern framework of abstract algebra, presenting each argument in its simplest and purest form, and stripping the theory from any unnecessary ballast, he manages to teach the subject in an utmost accessible, inspiring and profound manner. Many contemporary textbooks on Galois theory need hundreds of pages to reach a comparable depth of exposition, alas with much less lucidity, elegance ,and paedagogical effect. This is why one can still learn from a grandmaster like Emil Artin, and why the present classic will maintain its everlasting significance also in the future.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Algebra with Galois Theory

- Cover Cover11
- General editor information ii3
- Title Page iii4
- Contents v6
- Editors’ Note vii8
- Groups 110
- Rings and fields 1120
- Polynomials. Factorization into primes. Ideals 2130
- Solution of the general equation of 𝑛th degree. Residue classes. Extension fields. Isomorphisms 3342
- Galois theory 4958
- Polynomials with integral coefficients 8190
- The theory of equations 91100
- Back Cover Back Cover1137