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Algebra (Graduate Texts in Mathematics) 3rd Edition

by Serge Lang (Author)
4.1 out of 5 stars 30 customer reviews
ISBN-13: 978-0387953854
ISBN-10: 038795385X
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Product Details

  • Series: Graduate Texts in Mathematics (Book 211)
  • Hardcover: 914 pages
  • Publisher: Springer; 3rd edition (June 21, 2005)
  • Language: English
  • ISBN-10: 038795385X
  • ISBN-13: 978-0387953854
  • Product Dimensions: 6.1 x 1.9 x 9.2 inches
  • Shipping Weight: 3.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (30 customer reviews)
  • Amazon Best Sellers Rank: #133,411 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

4.0 out of 5 starsa useful advanced graduate reference on algebra
By mathwonk on April 4, 2006
Format: Hardcover
As others have said, this is not a book to begin learning algebra, but is a necessary book for most students to have on their shelves. Why is that? Basic topics are discussed from scratch in this book from the most advanced possible viewpoint. Hence few can learn them here for the first time, but no one can graduate to professional status without eventually arriving at this perspective.

In particular the categorical point of view is simply essential to a research mathematician to acquire at some point, and Lang uses it here from the beginning, while Dummitt and Foote place it in appendix II, after page 800. So Lang's goal seems not to introduce basic algebra, but to provide essential algebraic facts not found elsewhere, and to give them all from a professional's perspective.

This is probably a third book on algebra in today's world, and that is assuming the student is pretty good. The only current book I know of out there that is really aimed at students and also written by a top professional is Artin. If you can, begin with Artin, then read Dummitt and Foote for topics Artin omits, then read Lang to see how you should view the same material and find things Dummitt and Foote left out.

Then you are ready to do research with these tools. For instance one of our research professors tells his students the prerecquisite for working in algebraic number theory is to become comfortable with algebra at the level of Lang. But our course in PhD prelim preparation for algebra will probably use Dummitt and Foote, just because it is a more feasible book for the students to read at that stage. Attempts to use Lang in trhe past have been disastrous.Read more ›
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5.0 out of 5 starsA worthwhile pain in the [behind]
By Jason Schorn on July 24, 2003
Format: Hardcover
I must concur with my fellow readers that in fact Langs Algebra text is extremely dry, the examples are sparse (as compared with, say, Hungerfords Graduate text), readers are left to fill in the gaps which exist within the majority of proofs and, finally, about the exercises; for the most part the exercises abound, they are challenging, non-trivial and in general are extensions of the material, which for whatever reason, have been relegated to the status of mere exercise. But for those who have a 'Solid' foundation in Algebra, preferably at the level of a Junior-Senior undergraduate who has completed courses in Linear Algebra, Modern/Abstract Algebra, then this text is worth its weight in gold. For those individuals who have either chosen to make Mathematics their career or those who are Mathematically gifted, a text of this stature must be appreciated for exactly those reasons I used to 'negatively' criticize this text. For example, when doing research at any level above that of advanced undergraduate, the researcher should have the confidence, temperance, skill and desire to fill in missing gaps within proofs since the ability to do so is an excellent gauge of how well one actually understands the given material. It would seem to logically follow from this that the researcher would then benefit from choosing a text that contained exercises, which were not trivial calculations or the requirement of proving somthing that is either routine or standard. Instead, major rewards, in the form of confidence and a deeper understanding, are a result of struggling through difficult problems and, in general, problems which lead you toward self-discovery, i.e. those which are extensions of the given material. For these reasons I highly recommend this text to all members of the Mathematical community who desire more bang for their buck since this will serve them well, both as a text for further study and as a lifelong reference.
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5.0 out of 5 starsThis will teach you how to run if you know how to walk
By A Customer on November 12, 2003
Format: Hardcover
Lang's algebra book is one of the best algebra books available today. I agree with what most other readers have said. Namely, this shouldn't be your first foray into the subject, the proofs are often terse and take a good amount of time to absorb and there is a conspicuous lack/obscurity of examples. To cite an example, he gives a non-singular projective group variety as an example of a certain group. I shall not give an example of a terse proof. Let's just say that it suffices to note that whenever he says something is 'obvious', the non-expert reader should be prepared to scribble on 4-5 sheets of paper if she wishes to understand why it's 'obvious'.
The core matter (groups, rings, fields, modules) is the same as that you'd find in any other book. As far as topics are concerned, there are just too many fascinating topics in Algebra to cover in one book - even in one like Lang. He covers a fairly wide assortment of topics though. For instance, he covers most of the commutative algebra one would find in Atiyah-Macdonald. He also has a chapter and half on Algebraic Geometry which provides a good preparation for a treatment of schemes like that in Hartshorne Chapter 2,3. His section on Galois theory is detailed and even gets into Galois Cohomology. His chapter on Valuations gets into the theory of Local Fields, but only just. The chapters on multilinear algebra and representation theory are fairly detailed. I talk about the section on Homological Algebra later.
Regarding category theory, Lang likes to phrase his definitions in the language of category theory for a reason. It's much much better this way. Category theory is an elegant way of describing some commonly occuring themes in Mathematics, particularly algebra.Read more ›
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Most Recent Customer Reviews

5.0 out of 5 starsOne of the Algebra Triumvarate Texts.

A very complete text - well written from a fully rigorous level. It is the foundation text of a solid understanding of Algebra. Read more

Published 2 months ago by mw
5.0 out of 5 starsFive Stars

good

Published 5 months ago by Vitaly Zaderman
5.0 out of 5 starsA very useful book! Although It was hard to read at ...

A very useful book! Although It was hard to read at first, it became a good reference once I got used to the structure of the book.

Published 7 months ago by YAYIFU
5.0 out of 5 starsThe algebraist's bible, or a graduate student's nightmare?

Lang has already firmly established a reputation for writing textbooks which, I find, more often than not, leave something to be desired. Read more

Published 8 months ago by supermanifold
5.0 out of 5 starsI enjoy it quite a bit.

I really like the book. It can be rough but every time I have sat down and really tried to figure out what Lang is doing in some proof, I come out having learned so much. Read more

Published 10 months ago by QQ
5.0 out of 5 starsGreat to have on my bookshelf

This is like an encyclopedia for algebra. You wouldn't want to read it in order to learn the material for the first time, but everything is in there so it makes a great reference.

Published 12 months ago by Dan
1.0 out of 5 starsproofs are not proofs

I'm not a mathematician, but even I can see that many of the basic proofs are incomplete, or misleading at best. Read more

Published 12 months ago by BB
5.0 out of 5 starsFive Stars

An excellent book to learn algebra, it covers many subjects and evidences the relationship betwen them.

Published 12 months ago by Laura Espinosa-Méndez
4.0 out of 5 starsA great reference book for algebraists

A great reference book for algebraists, but not great for learning out of. Very dense, but easy to look things up.

Published 18 months ago by Sara T
2.0 out of 5 starsOnly for experts (and maybe not even for them)

Had to go through most of this book for PhD course and I hated it. It contains zero motivation and explanation as to why did anyone ever explore these topics, e.g. Read more

Published 20 months ago by Nikola Adzaga

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