Table of Contents

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.

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S. Lang 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."--NOTICES OF THE AMS "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."--MATHEMATICAL REVIEWS From the reviews of the third edition: "The current third edition has grown again ! dealing with topics close to the author's heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields ! . This makes it a fascinating book to read ! . a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items." (Paul M. Cohn, Zentralblatt MATH, Vol. 984, 2003) "Lang's Algebra ! has gained an iconic status, due both to the comprehensiveness of its coverage and its ability to be authoritative and lively at the same time. ! a revolutionary work, changing the way in which graduate algebra was taught. ! the author describes the book as 'very stable', indicating that there is little that he has wished to change. This confidence is reflected in the wider mathematical community, and ... this new printing deserves a place in every university departmental library." (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003)