Algebra - Third Edition - Lang Serge

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Résumé :
As I see it, the graduate course in algebra must primarily prepare students to handle the algebra which they will meet in all of mathematics: topology, partial differential equations, differential geometry, algebraic geometry, analysis, and representation theory, not to speak of algebra itself and algebraic number theory with all its ramifications." -Serge Lang, preface to the third edition 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, Algebra, Third Edition, by Serge Lang of Yale University, approaches the subject from a modern and comprehensive approach. Part 1 introduces the basic concepts of algebra. After covering these, the book splits in two major directions: the direction of algebraic equations including the Galois theory in part 2 and the direction of linear and multilinear algebra in parts 3 and 4. Ten years have passed since publication of the second edition of Algebra. this edition has been updated to include: ? many new examples and exercises ? many references to the contemporary mathematical literature and a number of unsolved problems that put students in contact with research. the abc conjecture may be the most spectacular of these ? an expanded chapter on representation theory, including Mackey's theorems. and a new section describing A the irreducible characters of GL, of a finite field, which is woven into the book in several contexts ? two new sections on elimination theory, complementing the existing section on the resultant In addition, the organization has been updated as follows: ? commutative algebra is integrated with algebraic sets and elimination theory ? all homological algebra topics now appear in part 4

Sommaire:
["THE BASIC OBJECTS OF ALGEBRA","Groups","Rings","Modules","Polynomials","ALGEBRAIC EQUATIONS","Algebraic Extensions","Galois Theory","Extensions of Rings","Transcendental Extensions","Algebraic Spaces","Noetherian Rings and Modules","Real Fields","Absolute Values","LINEAR ALGEBRA AND REPRESENTATIONS","Matrices and Linear Maps","Representation of One Endomorphism","Structure of Bilinear Forms","The Tensor Product","Semisimplicity","Representations of Finite Groups","The Alternating Product","HOMOLOGICAL ALGEBRA","General Homology Theory","Finite Free Resolutions."]