Algebra (book)

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For other uses, see Algebra (disambiguation).

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

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.[1]

Topics

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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 fourth part, Homological Algebra, covers general homology theory and finite free resolutions.

Audience and reception

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The Mathematical Association of America (MAA) states that undergraduate mathematics libraries have a copy of Algebra available.[2]

Reviews of Algebra appeared in The Mathematical Gazette in 1967 and 2003.[3][4]

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.[5]

References

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  1. ^ a b Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (3rd revised ed.), Springer-Verlag, p. 929
  2. ^ "Algebra", MAA Reviews, Mathematical Association of America, December 15, 2005, retrieved June 2, 2025
  3. ^ Brandstein, A. G.; Lang, Serge (January 1967). "Algebra". The American Mathematical Monthly. 74 (1): 103. doi:10.2307/2314094. ISSN 0002-9890. JSTOR 2314094.
  4. ^ 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.
  5. ^ Bergman, George (August 25, 2006), A Companion to Lang's Algebra, retrieved June 2, 2025