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Author Lang, Serge, 1927-2005.

Title Algebra / Serge Lang.

Published New York : Springer, [2002]


Location Call No. Status
 UniM Store ERC  512 LANG    DUE 01-03-21
Edition Rev. 3rd ed.
Physical description xv, 914 pages : illustrations ; 24 cm.
Series Graduate texts in mathematics ; 211.
Graduate texts in mathematics ; 211.
Bibliography Includes bibliographical references and index.
Contents Part 1 Basic Objects of Algebra -- Chapter I Groups 3 -- Chapter II Rings 83 -- Chapter III Modules 117 -- Chapter IV Polynomials 173 -- Part 2 Algebraic Equations -- Chapter V Algebraic Extensions 223 -- Chapter VI Galois Theory 261 -- Chapter VII Extensions of Rings 333 -- Chapter VIII Transcendental Extensions 355 -- Chapter IX Algebraic Spaces 377 -- Chapter X Noetherian Rings and Modules 413 -- Chapter XI Real Fields 449 -- Chapter XII Absolute Values 465 -- Part 3 Linear Algebra and Representations -- Chapter XIII Matrices and Linear Maps 503 -- Chapter XIV Representation of One Endomorphism 553 -- Chapter XV Structure of Bilinear Forms 571 -- Chapter XVI Tensor Product 601 -- Chapter XVII Semisimplicity 641 -- Chapter XVIII Representations of Finite Groups 663 -- Chapter XIX Alternating Product 731 -- Part 4 Homological Algebra -- Chapter XX General Homology Theory 761 -- Chapter XXI Finite Free Resolutions 835 -- Appendix 1 Transcendence of e and [Pi] 867 -- Appendix 2 Some Set Theory 875.
Summary "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 -- 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.
Subject Algebra.
ISBN 038795385X (alk. paper)