Algebra (Lang)

Short description: Graduate level textbook on algebra

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

Algebra is a graduate level textbook on Algebra written by Serge Lang, originally published by Addison-Wesley in 1965. It is now in its third edition, and is heavily cited, with over 10,000 citations in Google Scholar. The book has been described as having an enormous impact, single-handedly reorganizing and revitalizing the treatment of algebra.[1]

Serge Lang was awarded the Steele prize for exposition in 1999, the citation stating that Algebra is among his most famous texts.[2] The Mathematical Association of America (MAA) strongly recommends it for acquisition by undergraduate mathematics libraries.[3]

## Topics

The third edition[4] is divided into four parts. The first part, The Basic Objects of Algebra, covers groups, rings, modules and polynomials. Part Two, Algebraic Equations covers Field Theory but also has one chapter on Noetherian rings and modules. The third part, Linear Algebra and Representations includes chapters on the Tensor product of modules and on Semi-simplicity. The final part, Homological Algebra has a chapter on General Homology Theory and one on Finite Free Resolutions.

## Audience and reception

The book is intended for a one-year course at the graduate level. It is designed for readers who have had previous exposure to algebra in an undergraduate course.[4]

Reviews of the book are enthusiastic, saying since its first appearance it has gained an iconic status[5], achieve[s] an admirable and needed blend of several seemingly divergent facets of algebra[6], and The author has an impressive knack for presenting the important and interesting ideas of algebra in just the 'right' way.[7]

Professor George Bergman of Berkeley has written 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.[8]

## References

1. ↑ Jorgenson, Jay; Krantz, Steven G. (May 2006), "Serge Lang, 1927-2005", Notices of the AMS 53 (5): 538, https://www.ams.org/notices/200605/fea-lang.pdf
2. ↑ "Steele Prize for Mathematical Exposition: Serge Lang", Notices of the AMS 46 (4): 457-459, April 1999, https://www.ams.org/notices/199904/comm-steele-prz.pdf
3. ↑ Algebra, Mathematical Association of America, December 15, 2005, https://old.maa.org/press/maa-reviews/algebra, retrieved June 2, 2025
4. ↑ 4.0 4.1 Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, 211 (3rd revised ed.), Springer-Verlag, p. 929
5. ↑ Leversha, Gerry (July 2003), The Mathematical Gazette, 87, pp. 390-391
6. ↑ Brandstein, Gerry (January 1967), The Mathematical Gazette, 74, pp. 390-391
7. ↑ Algebra, Springer-Verlag, December 15, 2005, https://link.springer.com/book/10.1007/978-1-4613-0041-0, retrieved June 3, 2025
8. ↑ Bergman, George (August 25, 2006), A Companion to Lang's Algebra, https://math.berkeley.edu/~gbergman/.C.to.L/index.html, retrieved June 2, 2025

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