Basic Algebra: Groups, Rings and Fields

✍ Scribed by P. M. Cohn MA, PhD, FRS (auth.)

• Publisher: Springer-Verlag London
• Year: 2003
• Tongue: English
• Leaves: 468
• Edition: 1
• Category: Library

✦ Synopsis

Basic Algebra is the first volume of a new and revised edition of P.M. Cohn's classic three-volume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two self-contained, companion volumes, covering advanced topics in algebra for second- and third-year undergraduate and postgraduate research students.

In this first volume, the author covers the important results of algebra; the companion volume, Further Algebra and Applications, brings more advanced topics and focuses on the applications. Readers should have some knowledge of linear algebra and have met groups and fields before, although all the essential facts and definitions are recalled.

The coverage is comprehensive and includes topics such as:

- Groups

- lattices and categories

- rings, modules and algebras

- fields

The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks.

✦ Table of Contents

Front Matter....Pages i-xii
Sets....Pages 1-23
Groups....Pages 25-50
Lattices and Categories....Pages 51-78
Rings and Modules....Pages 79-130
Algebras....Pages 131-163
Multilinear Algebra....Pages 165-188
Field Theory....Pages 189-248
Quadratic Forms and Ordered Fields....Pages 249-306
Valuation Theory....Pages 307-345
Commutative Rings....Pages 347-396
Infinite Field Extensions....Pages 397-447
Back Matter....Pages 449-465

✦ Subjects

Algebra; Group Theory and Generalizations