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Algebra | 
 enlarge | Author: Serge Lang
Publisher: Springer
Category: Book
List Price: $74.95
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Avg. Customer Rating:  18 reviews
Sales Rank: 239994
Media: Hardcover
Edition: 3rd
Number Of Items: 1
Pages: 912
Shipping Weight (lbs): 3.1
Dimensions (in): 9.7 x 6.3 x 1.9
ISBN: 038795385X
Dewey Decimal Number: 512
EAN: 9780387953854
ASIN: 038795385X
Publication Date: June 21, 2005
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Product Description
"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." NOTICES OF THE AMS "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." MATHEMATICAL REVIEWS 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 added exercises and made numerous corrections to the text.
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| Customer Reviews: Read 13 more reviews...
A great reference book, not good to learn from May 14, 2007
1 out of 2 found this review helpful
As most of the books written by Prof. Lang, this book is a great compilation, it has what it needs to have, nothing more, nothing less. If you are in Math or any related field, and need a book to refresh your knowledge on Abstract Algebra, this is your book. though, I took a course in Grad School from this book, and I don't recomend it. Fortunatelly I still had the books from my undegrad courses (Rotman's Group Theory book is great), and I did remember the old courses anyway, but I really discourage the usage of this book as a lecture book.
 The way to learn algebra July 18, 2006
6 out of 11 found this review helpful
Most critisism of the book are based in the fact that topic are not treated in deep, and the reason is that there is no need to do that. Lang's porpouse is to introduce the reader to HIGHER ALGEBRA, while for example Dummit & Foote just end in Category Theory or Homological Algebra. He just introduce what he consider necessary to know about groups. Of course, if your porpouse is to learn, let's say Group Cohomology, then its good for you to know as much as possible about groups, modules and stuff, but Lang's try to focus on what HE consider is important to be known.
One has to have in mind that its easy to present the basic form of Cohomology or modules as Dummit does, but its has no continuity in the sense that will follow you to nothing, just to know some basic concepts. That's why i disagree with the people that say that is like an encyclopedia. Lang's development in Algebra is AMAZING. Ok, one can argue that it can be stated more ''friendly'' such as Galois Theory by Artin book does. But for Galois theory that's easy while in General Algebra is doesn't. Just take a look at Galois Theory section [which is, as every book, based on Artin works], there is nothing that is understandable in it, and its not an extensive work, because Lang will not USE in his HIGHER ALGEBRA.
The whole thing can be explained if you notice the Algebraic Number Theory book of Lang... you can consider Algebra as a preparation for his real book.
My education in math [academically] is minimal, but i always recommend this book, because when i get a subject i go directly to Lang and everything seems clear. Also, notation is really CLEAR and, comparing with authors like Jacobson, he doesn't mess with [unless necessary] formalizations.
So, my advice:
If you want to LEARN algebra, and work in algebra, READ LANG, READ LANG, READ LANG.
If you want to get some knowledge about algebra, and take a course, this is not your book.
This book grows on you. May 2, 2006
7 out of 7 found this review helpful
When I examined this book as an undergraduate I did not like it; often this is a sign that a book is poorly written, but in this case I just needed more background. Now I see this text as a gold-mine: clearly written, provocative, and rich in examples.
I find it refreshing that Lang does not get caught up in tedious proofs (one of my criticisms of Isaacs, another of my favourite algebra texts); anything that is tedious but not difficult, Lang leaves to the reader. Yet the book is not overly concise--a lot of ideas are explained in depth.
This book serves as an excellent reference for several reasons. First of all, it's unlike any other algebra book. The choice of topics is unusual; it will certainly expose you to some things you haven't seen before, but at the same time, it is not a comprehensive slice of modern algebra (it doesn't even mention lattices). However, the best aspect of it are the presence of examples, something sorely lacking from most other abstract algebra texts. Whenever a new concept is introduced, Lang presents a variety of examples from material elsewhere in the book as well as other fields of mathematics. These examples alone make this book precious. Although the biggest exercise is just reading and understanding the book, the exercises at the end of each chapter open up a whole other world; they are quirky and creative like the rest of the text.
I recommend this book for any serious mathematician to add to their collection. However, it would be waste of time to read it until you already know a great deal of mathematics. This is one of those books that becomes a must-read once have already read 25 or so other serious math books.
a useful advanced graduate refernce on algebra April 4, 2006
27 out of 30 found this review helpful
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.
Nonetheless, even students who found Lang a frustrating text, still use it as a necessary reference, and even find it has too little.
Just compare the treatment of groups in Lang and Dummitt and Foote. Lang covers the whole subject in more depth in 60 pages (2nd edition) while D/F use up over 220 pages on groups, and still do not introduce the categorical point of view, and in particular do not prove the existence of "direct sums" i.e. coproducts (which they do not even define), of groups.
So if you only have Lang, you will almost surely not see enough detail to understand the material, and if you only have D/F you will not see it from quite the right perspective, and will still not know some basic results.
Lang's book has numerous frustrating traits, misprints, errors, many uses of the word "obvious" for arguments that need a great deal of filling in, careless slipups ad nauseam, dyslexic things like saying clearly when to use product as opposed to coproduct, then getting it precisely backwards himself. or a whole discussion of Galois groups as permutations of roots of polynomials while forgetting to assume the polynomial is separable.
Your margins in Lang will be full of corrections, comments and added details, but now and then he will make something so clear in a word or two, that it will forever seem easy to you. In sum it is a locally flawed and carelessly written book, but globally impressive, and one for which there is no adequate substitute to my knowledge. Not least, Addison Wesley has always done a good job of making the type look beautiful on the page. The integrity of some recent bindings of course is another story.
Almost perfect! January 18, 2006
5 out of 7 found this review helpful
I have owned this book for many years now and I find that even after I have learned a topic in Lang or elsewhere, I still find that yet another careful reading of Lang will rearrange my thinking. I hear and read a lot of people complaining about this book, and I think most criticisms come from not having enough patience or energy to climb the book. (Yes, reading this is more like climbing!) There are few better things that you can do for yourself than hanging out with Lang.
The book does deserve some criticisms. His chapter on groups is just too small and insubstantial. Go elsewhere for that, like Rotman. The real purpose of that chapter is to introduce Category Theory, and it takes the wrong tack a few times there, I feel. So learn category theory somewhere else too. And all algebra books fail to explain what the algebra is good for. This one is no different. It is a shame because too many people think that Algebra is mostly for algebraists. But the truth is you can't do anything great without algebra.
The chapters on Homology theory are good in places, and the places where they are not so good, try the book by Weibel.
So, yeah, he is often a bit terse and leaves steps out. That's just an invitation to think things over. And it keeps the text clean. He is respecting you, honoring you, inviting you to the real party. He's not cheating you. He's giving you the real goo! You want the real goo, don't you?
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