# Algebraic Structures

• George R. Kempf

1. Front Matter
Pages I-IX
2. George R. Kempf
Pages 1-12
3. George R. Kempf
Pages 13-24
4. George R. Kempf
Pages 25-34
5. George R. Kempf
Pages 35-41
6. George R. Kempf
Pages 42-52
7. George R. Kempf
Pages 53-64
8. George R. Kempf
Pages 65-77
9. George R. Kempf
Pages 78-83
10. George R. Kempf
Pages 84-94
11. George R. Kempf
Pages 95-105
12. George R. Kempf
Pages 106-114
13. George R. Kempf
Pages 115-120
14. George R. Kempf
Pages 121-127
15. George R. Kempf
Pages 128-130
16. George R. Kempf
Pages 131-135
17. George R. Kempf
Pages 136-138
18. George R. Kempf
Pages 139-140
19. George R. Kempf
Pages 141-143
20. George R. Kempf
Pages 144-149
21. George R. Kempf
Pages 150-157
22. Back Matter
Pages 158-166

### Introduction

The laws of composition include addition and multiplication of numbers or func­ tions. These are the basic operations of algebra. One can generalize these operations to groups where there is just one law. The theory of this book was started in 1800 by Gauss, when he solved the 2000 year-old Greek problem about constructing regular n-gons by ruler and compass. The theory was further developed by Abel and Galois. After years of development the theory was put in the present form by E. Noether and E. Artin in 1930. At that time it was called modern algebra and concentrated on the abstract exposition of the theory. Nowadays there are too many examples to go into their details. I think the student should study the proofs of the theorems and not spend time looking for solutions to tricky exercises. The exercises are designed to clarify the theory. In algebra there are four basic structures; groups, rings, fields and modules. We present the theory of these basic structures. Hopefully this will give a good introduc­ tion to modern algebra. I have assumed as background that the reader has learned linear algebra over the real numbers but this is not necessary.

### Keywords

Algebra Algebraic structure Field Theory Group Theory algebra Logic Modern Linear Algebra Modules

#### Authors and affiliations

• George R. Kempf
• 1
1. 1.Department of MathematicsJohns Hopkins UniversityBaltimoreUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-322-80278-1
• Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 1995
• Publisher Name Vieweg+Teubner Verlag
• eBook Packages
• Print ISBN 978-3-528-06583-6
• Online ISBN 978-3-322-80278-1
• Buy this book on publisher's site