Algebra

Graduate Texts in Mathematics #211

by Serge Lang

This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has included additional exercises and made numerous corrections to the text.Comments on Serge Lang's "Algebra"

"Lang's "Algebra" changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books."

—From the April 1999 NOTICES OF THE AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books

"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." — From MATHSCINET's review of the first edition

Genres: Mathematics, Algebra, Reference, Textbooks, Science, Nonfiction

Paperback

First published December 1, 1965

About the author

Serge Lang was an influential mathematician in the field of number theory. Algebra is his most famous book.

Librarian Note: There is more than one author in the GoodReads database with this name. See this thread for more information.

Reviews

[Kat · Rating 2 out of 5]

Not exactly a light read. Very heavy book, good for hitting people with.

[Woflmao · Rating 2 out of 5]

This is the kind of book which people love who already know everything that's in it (and then they pretend this is the way they would have liked to learn it).
Lang's "Algebra" is a sterilised accumulation of algebraic facts, and it makes a good algebra encyclopaedia.
To its credit, the book does cover a lot of material which one would otherwise have to look for in many different books, and I assume this is the main reason for its fame.
Unfortunately, the exposition follows the Bourbaki ideology, so it is practically useless as a textbook to learn from.

[Ruoxi Huang · Rating 5 out of 5]

the final boss of mathematics

[J C]

I'm reading this book in conjunction with an online lecture series on abstract algebra by Benedict Gross, a Harvard professor who was once the dean of Harvard undergraduate programme and then the dean of Harvard College. So I feel in safe hands, especially when this book looks as intimidating as it really is. Someone here mentioned that it was 'good for hitting people with' and I agree wholeheartedly, this is a real brick, at 900 pages, and a very unusual one at that, as bricks to my knowledge are usually of a red, earthy colour, whereas this one is yellow. I suppose this is an allusion to the fact that mathematics isn't really of this earth... (unlike what Tegmark claims...)

In any case, I'm learning abstract alg because I need to know what rings, ideals, and polynomials of multiple variables are (and how they behave) as these seem to be the main objects of study in algebraic geometry.

[John Langstaff · Rating 5 out of 5]

Excellent! Great exercises.

[Geoffrey Lee · Rating 2 out of 5]

I commend the reader who is able to get past the first chapter. While the book certainly contains a lot of information, it is presented in the most concise possible way (which sometimes can be an advantage, but often makes the proofs impossible to comprehend). The homework problems are challenging and time consuming. Most of them involve extending the (more basic) concepts presented in the text to deeper levels of abstraction. Therefore, I would recommend using this book for its exercises while having perhaps another algebra book to actually learn the subject (Hungerford's book is excellent).

[Charlie · Rating 5 out of 5]

I love Lang's Algebra, and fully understand that this makes me a minority, even in the algebra community. It's amazing as a reference, the exercises range from perfunctory to really hard (some of them reach far beyond the text, and include citations of research papers), and it's relatively readable, if a bit formulaic at times. To me this indicates an intent to expose the reader to both the fundamentals and some beautiful math.

[Cyrus · Rating 1 out of 5]

The very reason that I don't like it is my lack of understanding. Of course Lange did a great job, but not for this low level of sophistication!

[Kiyoshi Takeuchi · Rating 5 out of 5]

The chapters on field and Galois theory are what distinguish this book from others.

[Jingyuan · Rating 4 out of 5]

good but hard to understand text, syntax and notation is a bit weird for modern standards.

[dead letter office · Rating 2 out of 5]

i believe lang's purpose in writing this book was to emphasize his superiority to mathematics graduate students. mission accomplished. read it if you already know everything in it, or if you enjoy hieroglyphics.

[Tim · Rating 3 out of 5]

as far as Lang goes, it's not bad, that is to say, this book would be horrible to learn from but as a reference, it's pretty decent.

[sqrt2 · Rating 5 out of 5]

good stuff, i didn't read it like a novel though, i just used as a reference book, i enjoyed it