Ebook: Introduction to Algebra
Author: R. Kochendörffer (auth.)
- Tags: Mathematics general
- Year: 1981
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
This book is intended as a textbook for an undergraduate course on algebra. In most universities a detailed study ·of abstract algebraic systems commences in the second year. By this time the student has gained some experience in mathematical reasoning so that a too elementary book would rob him of the joy and the stimulus of using his ability. I tried to make allowance for this when I chose t4e level of presentation. On the other hand, I hope that I also avoided discouraging the reader by demands which are beyond his strength. So, the first chapters will certainly not require more mathematical maturity than can reasonably be expected after the first year at the university. Apart from one exception the formal prerequisites do not exceed the syllabus of an average high school. As to the exception, I assume that the reader is familiar with the rudiments of linear algebra, i. e. addition and multiplication of matrices and the main properties of determinants. In view of the readers for whom the book is designed I felt entitled to this assumption. In the first chapters, matrices will almost exclusively occur in examples and exercises providing non-trivial instances in the theory of groups and rings. In Chapters 9 and 10 only, vector spaces and their properties will form a relevant part of the text. A reader who is not familiar with these concepts will have no difficulties in acquiring these prerequisites by any elementary textbook, e. g. [10].
Content:
Front Matter....Pages I-X
Basic concepts....Pages 1-19
The integers....Pages 20-39
Groups....Pages 40-112
Rings. Integral domains....Pages 113-150
Polynomials....Pages 151-182
Fields....Pages 183-242
Galois theory of equations....Pages 243-266
Order and valuations....Pages 267-284
Modules....Pages 285-335
Algebras....Pages 336-378
Lattices....Pages 379-406
Back Matter....Pages 407-414
Content:
Front Matter....Pages I-X
Basic concepts....Pages 1-19
The integers....Pages 20-39
Groups....Pages 40-112
Rings. Integral domains....Pages 113-150
Polynomials....Pages 151-182
Fields....Pages 183-242
Galois theory of equations....Pages 243-266
Order and valuations....Pages 267-284
Modules....Pages 285-335
Algebras....Pages 336-378
Lattices....Pages 379-406
Back Matter....Pages 407-414
....