Algebra (Lang)

Algebra
First edition
AuthorSerge Lang
LanguageEnglish
SeriesAddison-Wesley Series in Mathematics
SubjectAlgebra
GenreTextbook
PublisherAddison-Wesley
Publication date
1965
Pages508

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

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 Companion to Lang's Algebra, a 222 page book of notes collected when teaching Berkeley's basic graduate algebra course from Lang’s book.[7]

References

  1. ^ "Steele Prize for Mathematical Exposition: Serge Lang" (PDF), Notices of the AMS, 46 (4): 457–459, April 1999
  2. ^ "Algebra", MAA Reviews, Mathematical Association of America, December 15, 2005, retrieved June 2, 2025
  3. ^ a b Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (3rd revised ed.), Springer-Verlag, p. 929
  4. ^ Jorgenson, Jay; Krantz, Steven G. (May 2006), "Serge Lang, 1927-2005" (PDF), Notices of the AMS, 53 (5): 538
  5. ^ Brandstein, A. G.; Lang, Serge (January 1967). "Algebra". The American Mathematical Monthly. 74 (1): 103. doi:10.2307/2314094. ISSN 0002-9890.
  6. ^ Leversha, Gerry (July 2003). "Algebra, by Serge Lang. Pp. 914. £52.50 (hbk). 2002. ISBN 0 387 95385 X (Springer-Verlag)". The Mathematical Gazette. 87 (509): 390–391. doi:10.1017/s0025557200173310. ISSN 0025-5572.
  7. ^ Bergman, George (August 25, 2006), A Companion to Lang's Algebra, retrieved June 2, 2025
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