Algebra - 3rd edition

"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