Algebra [electronic resource] / by Serge Lang.

One The Basic Objects of Algebra -- I Groups -- II Rings -- III Modules -- IV Polynomials -- Two Algebraic Equations -- V Algebraic Extensions -- VI Galois Theory -- VII Extensions of Rings -- VIII Transcendental Extensions -- IX Algebraic Spaces -- X Noetherian Rings and Modules -- XI Real Fields -- XII Absolute Values -- Three Linear Algebra and Representations -- XIII Matrices and Linear Maps -- XIV Representation of One Endomorphism -- XV Structure of Bilinear Forms -- XVI The Tensor Product -- XVII Semisimplicity -- XVIII Representations of Finite Groups -- XIX The Alternating Product -- Four Homological Algebra -- XX General Homology Theory -- XXI Finite Free Resolutions -- Appendix 2 Some Set Theory.

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.