Algebra (book)

Algebra is a graduate-level textbook on abstract algebra written by Serge Lang and was originally published by Addison-Wesley in 1965. Its intended audience is students in graduate-level courses and readers who have previously attended undergraduate-level algebra courses.

Topics

The third-edition is divided into four parts. The first part, The Basic Objects of Algebra, covers groups, rings, modules, and polynomials. The second part, Algebraic Equations, focuses on field theory and includes a chapter on Noetherian rings and modules. The third part, Linear Algebra and Representations, contains chapters on the tensor product of modules and semi-simplicity. The fourth part, Homological Algebra, covers general homology theory and finite free resolutions.

Audience and reception

The Mathematical Association of America states that undergraduate mathematics libraries have a copy of Algebra available.
Reviews of Algebra appeared in The Mathematical Gazette in 1967 and 2003.
Professor George Bergman of University of California, Berkeley wrote Companion to Lang's Algebra, a 222-page book of notes collected when teaching Berkeley's basic graduate algebra course from Lang’s book.