Algebra (Lang)

Algebra is a graduate level textbook on Algebra written by Serge Lang, originally published by Addison-Wesley in 1965.

Algebra

First edition
Author	Serge Lang
Language	English
Series	Addison-Wesley Series in Mathematics
Subject	Algebra
Genre	Textbook
Publisher	Addison-Wesley
Publication date	1965
Pages	508

Serge Lang was awarded the Steele Prize for exposition in 1999, the citation stating that Algebra is among his most famous texts.^[1] The Mathematical Association of America (MAA) strongly recommends undergraduate mathematics libraries have a copy of Algebra available.^[2]

Topics

The third edition is divided into four parts.^[3] 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 final part, Homological Algebra, covers general homology theory and finite free resolutions.

Audience and reception

The book was designed by Lang to be intended for a one year graduate level course and for readers who have previously studied algebra at an undergraduate level.^[3]

The book in its latest third edition lists over 10,000 citations on Google Scholar and has been noted as a common reference material for papers in algebra.^[4]

Algebra received praise from mathematicians Gerry Leversha and Gerry Brandstein in The Mathematical Gazette in its 1967 and 2003 issues respectively.^[5][6]

Professor George Bergman of Berkeley wrote a 222 page Companion to Lang's Algebra, a collection of notes compiled when teaching Berkeley’s basic graduate algebra course from Lang’s book.^[7]