This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."
Author(s): Serge Lang
Series: Graduate Texts in Mathematics 211
Edition: 3rd
Publisher: Springer
Year: 2005
Language: English
Pages: 914
Front Matter....Pages i-xv
Front Matter....Pages 1-1
Groups....Pages 3-82
Rings....Pages 83-116
Modules....Pages 117-172
Polynomials....Pages 173-220
Front Matter....Pages 221-222
Algebraic Extensions....Pages 223-259
Galois Theory....Pages 261-332
Extensions of Rings....Pages 333-354
Transcendental Extensions....Pages 355-375
Algebraic Spaces....Pages 377-412
Noetherian Rings and Modules....Pages 413-447
Real Fields....Pages 449-463
Absolute Values....Pages 465-499
Front Matter....Pages 501-501
Matrices and Linear Maps....Pages 503-552
Representation of One Endomorphism....Pages 553-570
Structure of Bilinear Forms....Pages 571-600
The Tensor Product....Pages 601-640
Semisimplicity....Pages 641-662
Representations of Finite Groups....Pages 663-729
The Alternating Product....Pages 731-758
Front Matter....Pages 759-760
General Homology Theory....Pages 761-834
Front Matter....Pages 759-760
Finite Free Resolutions....Pages 835-866
Back Matter....Pages 867-918
