Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-ix
2. Serge Lang
Pages 1-12
3. Serge Lang
Pages 13-53
4. Serge Lang
Pages 54-71
5. Serge Lang
Pages 72-111
6. Serge Lang
Pages 112-143
7. Serge Lang
Pages 144-157
8. Serge Lang
Pages 158-183
9. Serge Lang
Pages 184-198
10. Serge Lang
Pages 199-222
11. Serge Lang
Pages 223-243
12. Back Matter
Pages 245-259

### Introduction

This book, together with Linear Algebra, constitutes a curriculum for an algebra program addressed to undergraduates. The separation of the linear algebra from the other basic algebraic structures fits all existing tendencies affecting undergraduate teaching, and I agree with these tendencies. I have made the present book self contained logically, but it is probably better if students take the linear algebra course before being introduced to the more abstract notions of groups, rings, and fields, and the systematic development of their basic abstract properties. There is of course a little overlap with the book Lin­ ear Algebra, since I wanted to make the present book self contained. I define vector spaces, matrices, and linear maps and prove their basic properties. The present book could be used for a one-term course, or a year's course, possibly combining it with Linear Algebra. I think it is important to do the field theory and the Galois theory, more important, say, than to do much more group theory than we have done here. There is a chapter on finite fields, which exhibit both features from general field theory, and special features due to characteristic p. Such fields have become important in coding theory.

### Keywords

Galois theory Permutation algebra automorphism field homomorphism linear algebra matrices

#### Authors and affiliations

1. 1.Department of MathematicsYale UniversityNew HavenUSA

### Bibliographic information

• Authors Serge Lang
• Series Title Undergraduate Texts in Mathematics
• DOI https://doi.org/10.1007/978-1-4684-9234-7
• Copyright Information Springer-Verlag New York 1987
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-96404-1
• Softcover ISBN 978-1-4684-9236-1
• eBook ISBN 978-1-4684-9234-7
• Series ISSN 0172-6056
• Edition Number 1
• Number of Pages IX, 379
• Number of Illustrations 0 b/w illustrations, 1 illustrations in colour
• Topics
• Buy this book on publisher's site

## Reviews

From the reviews of the third edition:

"As is very typical for Professor Lang’s self demand and style of publishing, he has tried to both improve and up-date his already well-established text. … Numerous examples and exercises accompany this now already classic primer of modern algebra, which as usual, reflects the author’s great individuality just as much as his unrivalled didactic mastery and his care for profound mathematical education at any level. … The present textbook … will remain one of the great standard introductions to the subject for beginners." (Werner Kleinert, Zentralblatt MATH, Vol. 1063, 2005)