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Abstract Algebra, 2nd Edition Hardcover – January 1, 1999

ISBN-13: 978-0471368571 ISBN-10: 0471368571 Edition: 2nd

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Editorial Reviews

From the Back Cover

Key Benefit: The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises throughout to aid the reader's understanding. Key Topics: This edition includes substantial new material in areas that include: tensor products, commutative rings, algebraic number theory and introductory algebraic geometry. Also, includes rings of algebraic integers, semidirect products and splitting of extensions, criteria for the solvability of a quintic, and Dedekind Domains. --This text refers to an out of print or unavailable edition of this title.
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Product Details

  • Hardcover: 912 pages
  • Publisher: Wiley; 2 edition (January 1, 1999)
  • Language: English
  • ISBN-10: 0471368571
  • ISBN-13: 978-0471368571
  • Product Dimensions: 7.2 x 1.6 x 9.6 inches
  • Shipping Weight: 3.1 pounds
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (21 customer reviews)
  • Amazon Best Sellers Rank: #594,311 in Books (See Top 100 in Books)

Customer Reviews

The writing is clear and flows very well, particularly due to good ordering of topics.
Decio Luiz Gazzoni Filho
I feel overwhelmed and amazed each time I look for something, or just browse thru it, for fun, to compare, or just to challenge the book.
lim_bus
This is _THE_ book to pick for advanced undergraduates, especially for those who wish to learn on their own.
David Rudel

Most Helpful Customer Reviews

116 of 119 people found the following review helpful By Chan-Ho Suh on June 17, 2003
Format: 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).
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22 of 23 people found the following review helpful By Marisa Debowsky on December 13, 2001
Format: Hardcover
This book arose from the lecture notes of Dave Dummit and Richard Foote, both at the University of Vermont. I first encountered this book in Dummit's own graduate algebra I-II class and was swept away by the clarity in contrast with my previous classes. Both authors are excellent teachers, and their text is equally good. Really slick development of group and ring theory, in an intuitive manner, constantly working through examples with symmetric and dihedral groups. Also includes high-level algebra suited for topics courses. I highly recommend this text.
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32 of 37 people found the following review helpful By J. Wiley on December 30, 2002
Format: Hardcover
For a number of reasons this may not be the best book for undergraduate self-study:
1. No answers to problems (though I think this should be much less a problem for anyone doing abstract algebra at any level, I'll stay off the soapbox)
2. This book contains a lot of information beyond the basic (undergraduate) essentials, and as this extra information is quite densely packed into each part of the book, it might be tough to pick out the main points
3. The exercises stay (for the most part) at a relatively uniform/low level of difficulty, but the proof/calculation ratio is kind of high (still resisting soapbox-related urges ...)
I'm sure there are others; many have been mentioned in previous reviews.
For graduate-level self-study, however, this book is a dream. As mentioned above, it is overflowing with information at every turn, which keeps the stuff that's review interesting and the stuff that's new accessible (at this level students should have the toolbox to deal with examples and such that draw from analysis, topology, or what-have-you). It has chapters on commutative algebra, homology theory, and representation theory (of finite groups), and appendices on Zorn's lemma and category theory. The conversational style isn't distracting (a big issue for me), possibly because of the exceptional organization for a book covering so much. Finally, the authors have succeeded tremendously in presenting everything with a view toward its ultimate use by the reader further along into "the great mathematical beyond" (I apologize for using this phrase).
One complaint: I can't seem to find a bibliography...
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16 of 17 people found the following review helpful By Darin Brown on May 18, 2001
Format: Hardcover
This book tries to accomodate both advanced undergraduates and beginning graduates. It would be a good challenge for undergrads to look at, and it covers most of the important topics you would see in a first-year graduate class. It should be readable for graduate students (compared to, say....Lang). Lang, of course covers far more material, but then again,...this is much more readable. One thing which would be a minor complaint is that several central, important topics are relegated to exercises. This is fine for a lot of things you want to introduce, but certain concepts are so fundamental (such as inverse and direct limits, p-adics, trace and norm of field extensions, Hilbert's theorem 90, etc.) that need to be presented within the text. Of course, it could be just my viewpoint that these are such important things in the first place. Overall, it's very readable and I got a lot out of it, even if I don't use it as a regular reference. I can't help but comment on one of the previous reviewers criticism that the authors make a "mistake" in reference to subrings. The mistake is entirely the reviewer's, who failed to read closely. In this book, a "ring" is not required to have identity, so 2Z (or nZ) is in fact a subring of Z, and the claim about subrings is true. The reviewer assumed without reading closely that identity was required. Just felt like vindicating the authors on the point!
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