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Basic Algebra II: Second Edition (Dover Books on Mathematics), by Nathan Jacobson
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A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for more than three decades. Nathan Jacobson's books possess a conceptual and theoretical orientation; in addition to their value as classroom texts, they serve as valuable references.
Volume II comprises all of the subjects usually covered in a first-year graduate course in algebra. Topics include categories, universal algebra, modules, basic structure theory of rings, classical representation theory of finite groups, elements of homological algebra with applications, commutative ideal theory, and formally real fields. In addition to the immediate introduction and constant use of categories and functors, it revisits many topics from Volume I with greater depth and sophistication. Exercises appear throughout the text, along with insightful, carefully explained proofs.
- Sales Rank: #199101 in Books
- Published on: 2009-07-22
- Released on: 2009-07-22
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x 1.40" w x 6.10" l, 1.90 pounds
- Binding: Paperback
- 704 pages
Most helpful customer reviews
19 of 19 people found the following review helpful.
Excellent
By Timothy Chow
Basic Algebra II is much better organized than Basic Algebra I, and it is an outstanding reference for the algebra that every Ph.D. graduate student should know. Perhaps the decision to prove Wedderburn's theorem via Morita theory was unfortunate since it makes the former seem more inaccessible than it really is, but otherwise I cannot fault the exposition. One word of warning: if your main interest is algebraic number theory, then Lang's _Algebra_ is probably a better reference since Jacobson omits several topics that are crucial for the number theorist.
18 of 18 people found the following review helpful.
Not that basic
By Gene W. Smith
It is indeed not an undergraduate level book, but Jaconson I&II
form a great overall introduction to algebra for the budding
algebraist. We used Jacobson I as the intro algebra text for
graduate students at Berkeley, and it can be recommended for
first or second year students (and beyond.) It forms a part of]
the trilogy of "Don't Let the Name Fool You" of not that basic
mathematics book with Weil's Basic Number Theory and Serre's
A Course in Arithmetic.
16 of 16 people found the following review helpful.
A review and an anecdote
By a reader
I knew Nathan Jacobson; for us students he was a towering figure in mathematics, the creator/inventor/discoverer of the (Jacobson) Radical, and the author of Basic Algebra I and II, which even now are looking at me from their places in the bookshelf. Mine are well-thumbed copies, and I didn't even go on to study Algebra. A quick look through the book and you realize that there is a difference between "basic" and "elementary". Elementary is easy. For Jacobson, "basic" means "the things a person needs to know in order to start doing advanced research". Volume I covers more (shall we say) standard material: Groups, Rings, Modules, Galois Theory, Classical Groups, Algebras, and Boolean Algebras. Volume II revisits some of these topics in much greater detail, and goes beyond them: we go back to put modules and rings under the microscope, then Representation Theory of finite groups, Homological Algebra, Commutative Ideals, Field Theory and Valuation Theory, etc. Of course, these were the topics close to his heart, and he put himself into the book. It is almost an encyclopedia of what there is in Algebra, except that I find it insightful and readable. For example, consider the start of section 4.2 in my edition of the book: "From the point of view that we took in the previous section, the purpose of defining the radical of a ring is to isolate that part of the ring whose elements are mapped into 0 by every irreducible representation of the ring. Accordingly, we introduce the following ..." and the definition of the Jacobson radical follows. So, there you have it: explaining the *why* of a definition, and setting up the next topic in a natural way. Crystal clear, and it is like that for the whole book. Mind you, that does not make this an easy book to read. It just means that the author does a fantastic job to explain and motivate what is certainly very hard mathematics.
Now an anecdote, and it is a true story. The grocery chain Stop and Shop has outlets in Connecticut. At some point they decided to sell books from local authors, and they saw that a local Yale professor had books called Basic Algebra I and II, so they thought it would be nice to have them in stock to sell for school kids -- help the community, you know. Of course, the books sold zilch, and Stop and Shop priced the books to give them away. In the end the local graduate students were the ones to benefit from it, because they bought those books on the cheap.
Remember, Basic is not Elementary!
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