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I have done a fair amount of research concerning which abstract algebra book to "settle down into"; that is, I wanted to pick an algebra text and really commit to it as my "primary text," more or less, and I have chosen Dummit and Foote's 3rd edition of Abstract Algebra.

My goal is to obtain a solid foundation in algebra at the beginning graduate level (I am self-learning). I have gone through a fair amount of John Durbin's Modern Algebra (6th ed.), but I know this is more of a "warm-up text." I have heard of algebra books by Herstein, Artin, etc., but I am no longer interested in a comparative analysis.

What are the chief drawbacks of using Dummit and Foote's text as my primary algebra text?

I know it has been criticized for being somewhat bland, but that it has a ton of excellent problems and examples and is fairly encyclopedic. I am more interested in mathematical drawbacks. Do they leave out any important topics in modern algebra? Does the book have extensive errata? Basically, what are the downsides of using this text? Preferably, I'd like to hear from people who have used this text before and have some background in abstract algebra who can look at my question from a more retrospective outlook.

Daniel W. Farlow
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    It has almost no category theory. – Asinomás May 05 '15 at 22:46
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    I don't know if this is a disadvantage though. – Asinomás May 05 '15 at 22:47
  • @Gamamal Yes, that was one of the first things I noticed--there are only 8 pages devoted to it, and even those come in an appendix and are not treated in the main text. – Daniel W. Farlow May 05 '15 at 22:48
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    Did you choose Dummit and Foote over Hungerford? Or was Hungerford not part of your comparative analysis? I think Hungerford is one of the best math books ever. I also tried several in graduate school and settled on that one as by far the best. – Gregory Grant May 05 '15 at 22:49
  • Hungerford has about 30 pages on category theory. – Gregory Grant May 05 '15 at 22:50
  • @GregoryGrant I didn't so much choose it over Hungerford so much as I simply chose it. The enormous number of exercises and comprehensive treatment are the features that appealed to me the most, but like I said--I really would like to know some of the mathematical issues people might take with D&F. – Daniel W. Farlow May 05 '15 at 22:51
  • @GregoryGrant Hmm. The second appendix of the third edition is devoted to category theory and there are only 8 pages there. Is there a different section in the text that I may have missed somehow? – Daniel W. Farlow May 05 '15 at 22:53
  • @MagicMan That's strange, Chapter X in my copy is called "Categories" and it's 21 pages. There is also a section in Chapter I called "Categories: Products, Coproducts and Free Objects" that is 8 pages. So 29 pages altogether. – Gregory Grant May 05 '15 at 23:00
  • @MagicMan Just to be clear, I was referring to Hungerford, I think you may have misunderstood and thought I was talking about Dummit and Foote. – Gregory Grant May 05 '15 at 23:04
  • @GregoryGrant Ah, yes, you are right--I thought you were referring to D&F. That makes sense. Thanks for clarifying! – Daniel W. Farlow May 05 '15 at 23:06
  • There are category theory bits sprinkled throughout. It's certainly not a great text for learning category theory, but I found it to be good preparation for a more advanced study of the subject. At this level of understanding, I think that a very large wealth of category-flavored examples (which D&F provides) is more important than studying extremely general concepts. For instance, adjoint functors are far easier to learn when you've seen dozens of them. – Andrew Dudzik May 05 '15 at 23:07
  • I think people could better answer your question if you give an idea of what general direction you may be headed in. Are you going to study algebra itself in the long term or are you preparing for something that uses algebra like number theory, algebraic topology, etc.? – Gregory Grant May 05 '15 at 23:16
  • @GregoryGrant Studying algebra in the long term is really what I had in mind. I'm trying to round out my undergrad education with solid books like Rudin's POMA, Real and Complex Analysis, and Munkre's Topology, and then a good algebra text. D&F seemed like a good fit, but it sounds like maybe I should check out Hungerford as well. – Daniel W. Farlow May 05 '15 at 23:20
  • I see. Well, unless you go on to do something like algebraic geometry or algebraic topology, you probably don't need to spend an inordinate amount of time studying commutative algebra, or category theory. I don't think those subjects are too deep and interesting in and of themselves. Since you don't know where you're headed and time is finite, you should probably focus on the most broadly applicable topics. – Gregory Grant May 05 '15 at 23:23
  • @GregoryGrant What topics would you say those are? Is such a pursuit more appropriate using D&F or Hungerford? It sounds like Hungerford could give me a great foundation and would be manageable while it might take half my life to complete D&F. – Daniel W. Farlow May 05 '15 at 23:27
  • Well, I'd hate to dissuade you from D&F since I've only ever cursorily looked at it. But it is about twice as long as Hungerford. I honestly don't think anybody reads these books cover-to-cover. I think everybody reads the basic material on groups, rings, modules and Galois theory. Then people refer to the other stuff as needed when they actually use algebra in other subjects. You want to get to the point where you can pick stuff up quickly later, but you don't need to learn all the algebra you will ever need now before moving on. – Gregory Grant May 05 '15 at 23:31
  • @GregoryGrant Good points. Thanks for all of your feedback. I appreciate it. – Daniel W. Farlow May 05 '15 at 23:32
  • Good luck with it, I honestly believe math is the most empowering major you can do, the world really really needs more people with those skills. – Gregory Grant May 05 '15 at 23:35

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Dummit and Foote's Abstract Algebra text is definitely not lacking in terms of mathematical content. Although the comments above are correct when they say there is almost no category theory, the number of topics covered in the text makes up for it. I have the text in front of me and it totals 7 pages of category theory. On the other hand, I have found each main section of the text has a fairly good treatment of the respective topic. Here I am mainly talking about the Group Theory, Rings and Modules, and Field and Galois Theory sections. There are several chapters on more advanced topics at the end but from what I can tell those are pretty introductory. I would contend that if you wish to have a single textbook that is very comprehensive, relatively easy to follow, and all around good for learning Abstract Algebra, Dummit and Foote is the way to go.

If you already have a solid mathematical background though you may want to check out Serge Lang's Algebra, which is just as comprehensive but considered more of a "graduate level" text. It also includes more Category Theory if that is a factor.

Martin Sleziak
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T. Ochse
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