- Hardcover: 933 pages
- Publisher: Springer; 3rd rev. ed. 2002. Corr. 4th printing edition (Jan 8 2002)
- Language: English
- ISBN-10: 038795385X
- ISBN-13: 978-0387953854
- Product Dimensions: 2.4 x 1.6 x 0.5 cm
- Shipping Weight: 1.4 Kg
- Average Customer Review: 4.3 out of 5 stars See all reviews (3 customer reviews)
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Amazon Bestsellers Rank:
#180,581 in Books (See Top 100 in Books)
- #17 in Books > Science > Mathematics > Pure Mathematics > Group Theory
- See Complete Table of Contents
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Product Details |
Product Description
Review
S. Lang 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."—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 From the reviews of the third edition: "The current third edition has grown again … dealing with topics close to the author’s heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields … . This makes it a fascinating book to read … . a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items." (Paul M. Cohn, Zentralblatt MATH, Vol. 984, 2003) "Lang’s Algebra … has gained an iconic status, due both to the comprehensiveness of its coverage and its ability to be authoritative and lively at the same time. … a revolutionary work, changing the way in which graduate algebra was taught. … the author describes the book as ‘very stable’, indicating that there is little that he has wished to change. This confidence is reflected in the wider mathematical community, and ... this new printing deserves a place in every university departmental library." (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003)
Book Description
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. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet's review of the first edition: "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."
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most helpful customer reviews
3 of 3 people found the following review helpful
5.0 out of 5 stars
This will teach you how to run if you know how to walk,
By A Customer
This review is from: Algebra (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. His preliminary section on category theory provides a good foundation to study the rest of his book. Another advantage of using category theory is that this prepares the reader well for further study in Algebraic Geometry and Algebraic Number Theory where the language of category theory is ubiquitous. On a related note, the book contains all the homological algebra necessary to read Hartshorne's Algebraic Geometry which is indeed quite wonderful for the reader who's not prepared to fight through Eisenbud's encyclopedia on commutative algebra. One of the other reviewers mentioned that Lang sneers at categorical arguments by calling them 'abstract nonsense'. This isn't quite right. He does call them 'abstract nonsense' but not because he dislikes them or harbours any sort of negative feeling towards them. Rather, he does it because the term 'abstract nonsense' is the common and accepted name used to refer to such arguments. Indeed, it's roots can be traced back to Steenrod who was one of the founders of the subject.
2 of 2 people found the following review helpful
5.0 out of 5 stars
A worthwhile pain in the [behind],
By
This review is from: Algebra (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.
1 of 1 people found the following review helpful
3.0 out of 5 stars
Great reference, poor text,
By topoman "topoman" (Newark, California USA) - See all my reviews
This review is from: Algebra (Hardcover)
If you want to learn Algebra, get Artin or Shafarevitch (encyclopedic and much more understandable) or even van der Waerden. Lang does not write in a manner that's understandable by novices and is, in fact often obscure even for cognescenti. His definitions are often couched in the most abstract of category theoretical forms. Amazingly, after doing such, he spends his chapter on homological algebra sneering at such abstractions (He calls it "Abstract Nonsense").Also, be aware that the change in "editions" seems to consist mostly of adding extra exercises to fill out the page. Once you know the material, Lang's book becomes an excellent reference - even there, I'd recommend Bourbaki or the Russian "Encyclopedia of Mathematics" for full expositions.
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