Algebra

Serge Lang (auth.)9780387953854, 038795385X

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. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.

Comments on Serge Lang’s Algebra:
Lang’s Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books.
April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books.

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.
MathSciNet’s review of the first edition

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Table of contents :
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