Algebra (Lang)
{{promotional tone|date=June 2025}}
{{Short description|Graduate level textbook on algebra}}{{Infobox book
|italic title =
|name = Algebra
|image = File:Algebra (Lang) 1st edition.jpg
|border = yes
|caption = First edition
|author = Serge Lang
|language = English
|subject = Algebra
|genre = Textbook
|pub_date = 1965
|publisher = Addison-Wesley
|series = Addison-Wesley Series in Mathematics
|pages = 508
}}
{{italic title}}
Algebra is an graduate level textbook on Algebra written by Serge Lang, orginally published by Addison-Wesley in 1965. It single-handedly reorganized and revitalized the treatment of algebra, and has had "an enormous impact".{{r|obit}} It is now in its third edition, and according to Google Scholar has been cited over 10,000 times.
Serge Lang was awarded the Steele prize for exposition in 1999, the citation stating that Algebra is among his most famous texts.{{r|steele}} The Mathematical Association of America (MAA) strongly recommends it for acquisition by and undergraduate mathematics library. {{r|maa}}
Topics
The third edition{{r|third}} 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.{{r|third}}
Reviews of the book are enthusiastic, saying since its first appearance it has gained an iconic status{{r|leversha}}, ''achieve[s] an admirable and needed blend of several seemingly divergent
facets of algebra{{r|brandstein}}, and The author has an impressive knack for presenting the important and interesting ideas of algebra in just the 'right' way.{{r|springer}}
Professor George Bergman of Berkeley has written a 222 page Companion to Lang's Algebra, comprising
222 pages of notes compiled when teaching Berkeley’s basic graduate algebra course from Lang’s book.{{r|bergman}}
References
{{reflist|refs=
| last1 = Jorgenson
| first1 = Jay
| last2 = Krantz
| first2 = Steven G.
| title = Serge Lang, 1927-2005
| journal = Notices of the AMS
| volume = 53
| issue = 5
| page = 538
| date = May 2006
| url = https://www.ams.org/notices/200605/fea-lang.pdf
}}
| title = Steele Prize for Mathematical Exposition: Serge Lang
| journal = Notices of the AMS
| volume = 46
| issue = 4
| pages = 457-459
| date = April 1999
| url = https://www.ams.org/notices/199904/comm-steele-prz.pdf}}
| title = Algebra
| website = MAA Reviews
| publisher = Mathematical Association of America
| date = December 15, 2005
| url = https://old.maa.org/press/maa-reviews/algebra
| access-date = June 2, 2025}}
| last = Lang
| first = Serge
| title = Algebra
| publisher = Springer-Verlag
| series = Graduate Texts in Mathematics
| volume = 211
| edition = 3rd revised
| date = 2002
| page = 929}}
| title = Algebra
| website = Springer Nature Link
| publisher = Springer-Verlag
| date = December 15, 2005
| url = https://link.springer.com/book/10.1007/978-1-4613-0041-0
| access-date = June 3, 2025}}
| last = Leversha
| first = Gerry
| title = The Mathematical Gazette
| volume = 87
| issue = 509
| date = July 2003
| pages = 390-391}}
| last = Brandstein
| first = Gerry
| title = The Mathematical Gazette
| volume = 74
| issue = 1
| date = January 1967
| pages = 390-391}}
| last = Bergman
| first = George
| title = A Companion to Lang's Algebra
| website = MAA Reviews
| date = August 25, 2006
| url = https://math.berkeley.edu/~gbergman/.C.to.L/index.html
| access-date = June 2, 2025}}
}}
Category:Mathematics textbooks