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.

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    $\begingroup$ It has almost no category theory. $\endgroup$ – HereToRelax May 5 '15 at 22:46
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    $\begingroup$ I don't know if this is a disadvantage though. $\endgroup$ – HereToRelax May 5 '15 at 22:47
  • $\begingroup$ @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. $\endgroup$ – Daniel W. Farlow May 5 '15 at 22:48
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    $\begingroup$ 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. $\endgroup$ – Gregory Grant May 5 '15 at 22:49
  • $\begingroup$ Hungerford has about 30 pages on category theory. $\endgroup$ – Gregory Grant May 5 '15 at 22:50

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.


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