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Recommend an Algebra book 
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#1
May711, 10:27 AM

P: 9

I have just finished my first course in Abstract Algebra. I was wondering if anyone could recommend a book that goes deeper into the subject. We covered groups and rings, but not much else after that.
Also, this is a really cool forum. 


#2
May711, 07:08 PM

P: 361

What text did you use? Also, your algebra text may cover other topics that you could study.



#3
May711, 07:41 PM

P: 183

Many people in this forum like the books by Serge Lang. He has several algebra books, basic to very advanced.



#4
May711, 07:59 PM

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P: 9,470

Recommend an Algebra book
i recommend algebra by Michael Artin of MIT, the book he developed from his sophomore MIT math major class.
I also have a free book on my website, notes for math 84345, and another: notes for math 8000[6]. http://www.math.uga.edu/~roy/ but Mike's book is better than mine, because he understands the subject better, and he taught the course several times and polished his book. 


#5
May711, 09:33 PM

P: 948




#6
May811, 11:41 AM

P: 17

One of the most beautifully motivated (and rigorous!) books I have ever seen on this topic is "Rings, Fields, and Groups" by Allenby. (It's the text used, IIRC, at Oxford.)



#7
May811, 12:39 PM

P: 9

Hi;
It depends on how much rigour you're looking for. As light reading, Pinter's book is great. It's written conversationally, so you can easily get through it in a short period of time. I'd recommend that you read it before you get into any of the heavier books. Then I'd recommend reading Dummit & Foote, it's generally accepted as a sort of classic introductory text in abstract algebra. If you've already been introduced rigorously to algebra and are comfortable without being 'babied' (I don't mean this in a bad way! I love being babied by books!) then by all means skip Pinter and go on to Dummit & Foote. Artin's book is also a classic. EDIT: Allenby is great too! Hope this helps. 


#8
May811, 05:49 PM

P: 9

Wow, lots of replies. Thanks guys.
The text that we used was the one by Fraleigh, but I don't like it too much. I found the exercises in the book were lacking in difficulty, at least up to where I left off. We covered groups, group actions, rings, homomorphisms, quotient rings/groups, integral domains and fields. We squeezed in a little bit on polynomials but we may as well have not gone over it. I will check out all of the recommendations, and if anyone has any other recommendations, the please let me know! Thanks again everyone. 


#9
May1011, 05:01 PM

P: 948

^ sounds like herstein's topics in algebra might be a good alternative, & if that's still too easy or basic, there's hungerford. the irritating thing with herstein though is that he denotes a function by xf, where other books have f(x). I guess it isn't a big deal. anyway besides that, he deliberately puts problems from later sections into the problem sets, maybe as soon as a reader can understand what it asks, just to see if anyone can figure out if it's possible to solve it without the firepower from later on in the text.



#10
May1011, 05:26 PM

P: 367

If you already finished a course then I recommend Jacobson basic algebra.



#11
May1011, 05:32 PM

Mentor
P: 18,219

I also recommend Dummit & Foote very highly! It contains a LOT of material and it is very interesting. Not for the beginner, but since you already took a course on it, you're not a beginner anymore.
And be assured, the exercises in Dummit & Foote do not lack in difficulty!! 


#12
May1011, 11:20 PM

P: 9

I ended up buying Artin's book as well as Rudin's book on Analysis and Munkres' book on Topology since I'll be taking those two courses next fall.
I also considered Dummit and Foote as well as Jacobson and still might get one or the other. Again, thanks for the responses. 


#13
May1111, 03:05 AM

P: 534



#14
May1211, 11:04 PM

P: 9

These links will be very helpful, thanks a lot. I try and do a lot of selfstudying but there's always an issue of not knowing if I'm doing everything right or if I really understand everything.



#15
May1311, 04:00 AM

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#16
Jun1311, 02:34 PM

P: 104

This was a month ago, I know, but I'm wondering how Artin's been working for you so far. I've been considering picking it up so I can really learn the material at a high level before my class this Fall.



#17
Jun1311, 09:23 PM

P: 9

I thought I would have plenty of time to study it this summer but I'm taking 3 courses that are fairly work intensive, although not particularly difficult. I also chose to start studying Topology first, and that's also been progressing much slower than I expected. =/ I'm sure you could learn a lot from it though if you are particularly diligent. 


#18
Jun1411, 03:57 AM

P: 261

In any case, I found Dummit and Foote's treatment of Galois theory to be much better written, to be honest with you, I am going to refresh my Algebra over the summer and I think I'll be using Dummit and Foote as my next level up from Fraleigh. Just remember, harder books are not necessarily better, while I would never want to have an "Abstract Algebra  Lite" course/text, I do like my books to be very clear and very readable. I think it's better to really understand the subject by working through some easier and clearer texts. 


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