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I want to purchase a book for Abstract Algebra but am too confused at the time that which one should I go for . Based on whatever I have gathered from web it seems :

  • Dummit and Foote.
  • Fraleigh.
  • I.N. Herstein.
  • Gallian.

are some goto books for a beginner , but few of my friend recommended some other books like :

  • Dan Saracino
  • Beachy
  • Hungerford
  • M. Artin

Because of which I am even more confused now. I have learned Linear Algebra, Real Analysis ,PDE ,Calculus of Variations at an Undergraduate level (if it helps). I want a book that contains everything that one should know about Abstract Algebra at an Undergraduate level and is fun to read , with good examples , great exercise section.So HELP ME PICK ONE .

  • If possible can you arrange them in order of your personal preference(with respective reasoning)?
  • What book did you read?
  • What are your experiences regarding that ?
  • Is there any other book you got to know about later that you find even more good and comprehensive ?

(I will be purchasing a Indian print of one of these 8 books as they are comparatively way cheaper than their respective counterparts.)

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    $\begingroup$ I personally like Dummit and Foote. $\endgroup$ Aug 15 '21 at 16:03
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    $\begingroup$ @masterOFnone You don't need to read all of it, just the parts that interest you. For example, it has a minichapter on algebraic geometry. You may want to skip that. $\endgroup$ Aug 15 '21 at 16:38
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    $\begingroup$ Fraleigh is ridiculously simplistic for someone with your background. Dummit and Foote, Artin and Herstein are all reasonable for someone with that background. My feeling is that D-F tries to be too comprehensive considering the level it's aimed for, Artin has some really good motivation and discussion, I think most people who learn from it enjoy it a lot. But I'm going to say something people might sometimes be reluctant to say clearly. A lot depends on your level of ability in math. If you have a high level of ability, there's no reason you shouldn't jump into a book like Jacobson instead. $\endgroup$
    – Anonymous
    Aug 23 '21 at 15:46
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    $\begingroup$ Also, beware of the current Indian edition of Artin. It's a completely mangled version of the original text. If you can get the earlier PHI Indian edition, the content should be identical to the original American version. Jacobson is published by Dover, so is really cheap. $\endgroup$
    – Anonymous
    Aug 23 '21 at 15:51
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    $\begingroup$ An alternative at an intermediate level of difficulty between Artin and Jacobson would be Algebra by Godement. The chapter on logic isn't good, but the rest is great. $\endgroup$
    – Anonymous
    Aug 23 '21 at 19:31
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I'm partial to a different book: Algebra, by Siegfried Bosch. The original is in German, but there is a translated edition. The book can actually be read like a book in the sense that Bosch actually connects the dots between all the definitions and theorems. Which is essential for self study, imho. He also has an informal discussion of the contents of each chapter before driving into the technicalities, so you actually know what the point of each chapter is. There are also very good exercises, though only some of them come with solutions.

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Hungerford’s book is very good in my opinion. Very well written but unfortunately cheap paper.

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$1.$ If possible can you arrange them in order of your personal preference(with respective reasoning)?

The only ones listed with which I'm familiar are the Dummit and Foote and Gallian texts, so no, unfortunately I can't rearrange them.

$2.$ What book did you read?

I've read An Introduction to Abstract Algebra with Notes to the Future Teacher by Olympia Nicodemi and Contemporary Abstract Algebra by Joseph Gallian. It's technically not a book, but I did have comprehensive class notes from a graduate course in abstract algebra through University of Illinois at Urbana-Champaign.

$3.$ What are your experiences regarding that?

The Nicodemi text is written for math education majors, so it doesn't go into much detail or cover many topics. I don't recommend it for any math majors not on an education track. I will never not recommend the Gallian text to others. Joseph Gallian presents many topics and applications while maintaining a flow that is clear and understandable. The exercises are reasonable and a good representation of each chapter's content. I would place this book at a later undergraduate/early graduate level. It contains information specifically on groups, rings, and fields. I actually recommended this text to my undergraduate advisor as a replacement for the Nicodemi text; he took me up on it and it's been going well so far. The class notes from UIUC were fantastic. Sometimes they were dense and cryptic, but once you get past that it goes fairly well.

$4.$ Is there any other book you got to know about later that you find even more good and comprehensive?

I suppose the "later" book for me was Gallian. I used it mainly as supplemental knowledge. I found a copy of Dummit and Foote online; it is enjoyable, but it gets technical quite fast.

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  • J.J. Rotman - First Course in Abstract Algebra, very readable.
  • Battacharya, Jain and Nagpaul - Basic Abstract Algebra, contains Groups, Rings and Modules and more, very readable.
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My personal favorite is Aluffi's Algebra: Chapter 0. It covers a lot of topics starting from the very elementary ones (you can skip those) and diving as deep as Homological Algebra. Furthermore, I personally find the writing style of Aluffi just excellent. The book contains a lot of concrete examples as well as a number of quality exercises of varying difficulty. Unfortunately, no solutions are provided, just hints for some of the more difficult exercises.

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