Can anyone recommend a deeper Algebra book beyond Fraleigh?

[Stylish]

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.

 

[Petek]

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

 

[brocks]

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

 

[mathwonk]

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 843-4-5, 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.

 

[fourier jr]

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.

what topics did you cover, beyond groups & rings? did you do fields, polynomials, quotient groups/rings, homomorphisms, structure theorems or was it more or less just an intro?

 

[aneesh.mulye]

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.)

 

[Gingia]

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.

 

[Stylish]

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.

 

[fourier jr]

^ sounds like herstein's topics in algebra might be a good alternative, & if that's still too easy or basic, there's https://www.amazon.com/dp/0387905189/?tag=pfamazon01-20. 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.

 

[deluks917]

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

 

[micromass]

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!

 

[Stylish]

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.

 

[sponsoredwalk]

The video lectures on both Linear & abstract algebra on this site use Artin's book,
their topology video lectures use Munkres & this video course uses Rudin's PoMA.
Should be a helpful supplement for self study.

 

[Stylish]

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

 

[Sankaku]

These Harvard videos also follow Artin:

http://www.extension.harvard.edu/openlearning/math222/

 

[Chaostamer]

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.

 

[Stylish]

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.

I hate to disappoint, but I actually haven't looked at it yet, sorry.

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.

 

[hitmeoff]

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.

Certianly Fraleigh is the clearest and most forgiving Abstract Algebra book out there (except the Galois THeory stuff, which could use some work). ANd while the "computation" and "concepts" problems are pretty easy, some of those Theory question are (at least to me) fairly difficult. I took an entire year long series with a professor known to be very tough, in a department that has a reputation for being very intense on math major...and the prof assigned some of the "theory" problems from Fraleigh (as well as some of his own) and even the Grad students would look at the question and shake their heads at the general difficulty of our homework sets.

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.