Abstract Algebra (Hardcover)

by David Dummit (Author), Richard M. Foote (Author) "Some results and notation that are used throughout the text are collected in this chapter for convenience..." (more)
Key Phrases: nonprincipal irreducible character, nonpivotal columns, modules whose annihilators, Euclidean Domain, Unique Factorization Domain, Fundamental Theorem (more...)

Editorial Reviews

Product Description

• Accessible to undergraduates yet its scope and depth also make it ideal for courses at the graduate level.
• Over 1500 exercises, many with multiple parts, ranging in scope from routine to fairly sophisticated, and ranging in purpose from basic application of text material to exploration of important theoretical or computational techniques.
• The structure of the book permits instructors and students to pursue certain areas from their beginnings to an in-depth treatment, or to survey a wider range of areas, seeing how various themes recur and how different structures are related.
• The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.
• Contains many topics not usually found in introductory texts. Students are able to see how these fit naturally into the main themes of algebra. Examples of these topics include:
• Rings of algebraic integers
• Semidirect products and the theory of extensions
• Criteria for Principal Ideal Domains
• Criteria for the solvability of a quintic
• Dedekind Domains
--This text refers to an out of print or unavailable edition of this title.

From the Publisher
This text is designed to give students insight into the main themes in abstract algebra. Early introduction to recurring notions such as homomorphisms, isomorphisms, actions, and classifications provides a natural flow for the development of basic abstract algebra. Students are immediately exposed to concepts the way an algebraist (or mathematician) envisions and works with them.

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Product Details

• Hardcover: 658 pages
• Publisher: Simon & Schuster (November 1990)
• Language: English
• ISBN-10: 0130047716
• ISBN-13: 978-0130047717
• Product Dimensions: 9.6 x 7.3 x 1.5 inches
• Shipping Weight: 2.7 pounds
• Average Customer Review: 4.1 out of 5 stars See all reviews (37 customer reviews)
• Amazon.com Sales Rank: #1,631,210 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

73 of 74 people found the following review helpful:

5.0 out of 5 stars You'll get a lot of mileage out of it, June 17, 2003

By	Chan-Ho Suh (Davis, CA USA) - See all my reviews (REAL NAME)

This review is from: Abstract Algebra, 2nd Edition (Hardcover)

Most of the reviews have been positive, and basically explain the strengths of the book, but I thought some would appreciate hearing what someone, like me, who has gone through most of the material in the book over the last three and half years, would say.

This is the only book I bought as an undergraduate that I still look at today. All my other undergrad texts are either stored away somewhere or gather dust on my bookshelf. The reason is simple: Dummit and Foote has stocked in one book almost all the basic algebra that is required for my study of 3-manifold theory. I suspect this is true of other fields also. By "basic algebra" I mean the key ideas and examples that are used in many different areas of mathematics.

Just recently, I needed to pick up some algebraic geometry in order to understand SL(2, C) character varieties. As usual, I went to my Dummit and Foote and found what I needed (for the most part). And also as usual, I will need to supplement that knowledge with some more advanced books.

A couple things about this book annoy me though: 1) the price -- however, I have certainly gotten my money's worth out of it over the years, so I can't really complain 2) Initially when I first got the book, the wealth of material in the book appeared intimidating and esoteric to me; however, nowadays I would say there isn't *enough* in this book. Oftentimes it seems that I get just a taste before the discussion of a topic ends. On the other hand, I am realistic, so I realize that this book is not meant to be encyclopedic but to introduce the reader to the more advanced topics.

I've yet to see another book that carries all the topics of this one, and remains fairly reader-friendly (as this one does).

31 of 33 people found the following review helpful:

5.0 out of 5 stars The book after Herstein, December 11, 2004

By	Michael B Williams "Brandon" (Brooklyn, NY) - See all my reviews

This review is from: Abstract Algebra (Hardcover)

I think I would only recommend this book to someone who has already had some exposure to algebra (or one especially gifted in mathematics). The beginning of the book is not too bad, but towards the end of Part I the pace quickens quite a bit. If you are willing to read over the text many times, and do all of the non-trivial exercises (there is an impressive olla podrida of algebra in them, most of which are the beginnings of some very deep ideas), then it should be a very rewarding experience. Namely because this is one of the most readable textbooks which covers everything from groups, rings, and fields to homological algebra and algebraic geometry. It is very rare to see this much material covered in one book, and for it to remain so structured (Rotman is an example of a book that covers a lot of material, but loses its structure somewhere).

20 of 22 people found the following review helpful:

3.0 out of 5 stars This book is rigorous, dense, and lacks answers to exercises, November 8, 1998

By A Customer

This review is from: Abstract Algebra (Hardcover)

It is a strong, rigorous introduction to abstract algebra, but I find it too intense for most undergraduates to fully grasp without studying for extraordinary amounts of time. None of the exercises have answers provided. so it isn't very useful for self-study. It is abstract in its very quintessence: it gives no examples of applications of the theorems. If you don't have a significant background in mathematical proofs and abstract logic, choose a more accessible text. But, if you can handle the level of rigor and abstraction, the text is very rewarding.