Recommend an Algebra book

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

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 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.

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

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.