Basic Abstract Algebra (Paperback)

by P. B. Bhattacharya (Author), S. K. Jain (Author), S. R. Nagpaul (Author) "The concept of set is fundamental in mathematics..." (more)
Key Phrases: defective picture tube, defective sound system, nonisomorphic abelian groups, Proof Let, Proof Suppose, Example Let (more...)

Editorial Reviews

Review
"...a thorough and surprisingly clean-cut survey of the group/ring/field troika which manages to convey the idea of algebra as a unified enterprise." Ian Stewart, New Scientist

Product Description
This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples.

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Product Details

• Paperback: 508 pages
• Publisher: Cambridge University Press; 2 edition (November 25, 1994)
• Language: English
• ISBN-10: 0521466296
• ISBN-13: 978-0521466295
• Product Dimensions: 8.8 x 6 x 1.3 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars See all reviews (8 customer reviews)
• Amazon.com Sales Rank: #738,986 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

11 of 12 people found the following review helpful:

4.0 out of 5 stars too concise in some parts, good elsewhere, April 12, 2004

By	Fourier Jr (Victoria, Canada) - See all my reviews

I picked this book up at my students' society used bookstore for $10, it turned out to be a pretty good bargain. However, there are some theorems where the authors say something is obvious & I didn't think so. It isn't very often though, the rest of the book is pretty good, and I was a bit surprised because I had only heard of the well-known authors like Gallian, Herstein, Lang, etc. It covers maybe 3 courses worth of material too, including groups, rings, fields, vector spaces & modules, Galois Theory (complete with every possible application!), and more advanced stuff like a separate chapter on modules (in addition to the section with vector spaces), tensor products and principal ideal domains. There are also complete solutions to the odd-numbered problems. This book is surprisingly good except in certain parts, I like it.

7 of 8 people found the following review helpful:

5.0 out of 5 stars A must for every math library, September 11, 2002

By	Scott M. Feldman (Rockaway Park, NY USA) - See all my reviews

This review is from: Basic Abstract Algebra (Hardcover)

Bhattacharya is very concise and readable for a very difficult subject, if you are new to abstract algebra. His proofs are complete and expert and his outline is great. Also his problems are useful

9 of 12 people found the following review helpful:

4.0 out of 5 stars Good but..., September 8, 2000

By	R. Ball (London W14, England United Kingdom) - See all my reviews (REAL NAME)

I agree this is a very clear and easily readable text but a graduate text it is not. One would need to know most of this material before starting graduate level. Lots of stuff is left out and I think a rather better book that is equally clear and readable etc. but much more comprehensive with more worked examples and historical motivation is Malik et.al. in McGraw-Hill "Fundamentals of A.A.".