Algebra (Lang)

Last updated
Algebra
Algebra (Lang) 1st edition.jpg
First edition
Author Serge Lang
LanguageEnglish
SeriesAddison-Wesley Series in Mathematics
SubjectAlgebra
GenreTextbook
Publisher Addison-Wesley
Publication date
1965
Pages508

Algebra is a graduate-level textbook on algebra (abstract algebra) written by Serge Lang. The textbook was originally published by Addison-Wesley in 1965. It is intended to be used by students in one-year long graduate level courses, and by readers who have previously studied algebra at an undergraduate level. [1]

Contents

Topics

The third edition is divided into four parts. [1] 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

Serge Lang was awarded the Leroy P. Steele Prize for exposition by AMS in April 1999. [2]

The Mathematical Association of America (MAA) recommends undergraduate mathematics libraries have a copy of Algebra available. [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. 1 2 Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (3rd revised ed.), Springer-Verlag, p. 929
  2. ↑ "Steele Prize for Mathematical Exposition: Serge Lang" (PDF), Notices of the AMS , 46 (4): 457–459, April 1999
  3. ↑ "Algebra", MAA Reviews, Mathematical Association of America, December 15, 2005, retrieved June 2, 2025
  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
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.