Looking for an Advanced Abstract Algebra Text

[JasonRox]

Does anyone know a good Abstract Algebra text?

I currently have the text by Gallian and quite frankly I give two stars out of five.

I'm looking for something that's more advanced, and well written.

Any recommendations will be greatly appreciated.

 

[devious_]

If you know linear algebra and want an advanced text, there's Herstein.

If you want an introduction to the basics (without reliance on linear algebra), i.e. group theory, ring theory and some field theory, and without overloading yourself, then there's Fraleigh. I personally think the chapters on group theory are very well done. I haven't looked at the later parts of the book that cover rings and fields, so I can't say much about them.

 

[fourier jr]

beginner's algebra:
abstract algebra -- herstein
intro to modern algebra -- gilbert/gilbert

intermediate algebra:
topics in algebra -- herstein

hardcore algebra:
noncommutative rings -- herstein
field theory & its classical problems -- hadlock
galois theory -- e. artin
algebra -- grove
algebra -- dummit/foote

 

[JasonRox]

beginner's algebra:
abstract algebra -- herstein
intro to modern algebra -- gilbert/gilbert
intermediate algebra:
topics in algebra -- herstein
hardcore algebra:
noncommutative rings -- herstein
field theory & its classical problems -- hadlock
galois theory -- e. artin
algebra -- grove
algebra -- dummit/foote

Great list.

 

[quantumdude]

then there's Fraleigh.

I will second that recommendation. We used Fraleigh in our abstract algebra class, and I enjoyed it very much.

 

[mattmns]

The book we used in my abstract algebra class this semester was: A first course in Abstract Algebra (2nd edition) by Joseph J Rotman. I think the general consensus in the class was that the book was bad. I felt there were too few examples and the book often discussed things that had nothing to do with the subject.

 

[MathematicalPhysicist]

you can always find some lecture notes at sites such as dmoz.org or search at sites of universities.
at dmoz, quite frankly there are a lot of material on abstract algebra.

 

[mathwonk]

my recommendations:

I think the best beginning general abstract algebra book for linear algebra, groups, rings, fields, modules, even basic group representations: is Algebra, by Michael Artin.

This a sophomore level book at MIT, hence a graduate book most places.

Another classic I like is Algebra by Van der Waerden.

Maybe the best pure linear algebra book is by Hoffman and Kunze.

I always had trouble learning from mike's dad Emil Artin's book, Galois theory, as it is too slick for me. Herstein is also very slick, goes in one ear and out the other. I do not like it much for beginners, but the problem sets are excellent for beginners, lots of fun special problems. But for insight into a topic, Herstein is not highly recommended by professionals I know. M. Artin on the other hand is outstanding.

At the graduate level, I like Dummit and Foote and, let's face it, it is hard to ignore Lang. But I have not taught from Dummit and Foote. Hungerford has good problems and examples, and is very systematic, but rather boring, and gives little insight into why things are true, in my opinion, but some of my best students did benefit from it in combination with other books.

For commutative algebra I like Zariski and Samuel for a long book, and Atiyah - MacDonald for a short book.

For homological algebra, MacLane is nice, or Northcott, or more rcently maybe Manin, if you want derived categories incuded.

start with artin. If that is too hard, try some of the books on other people's lists.

 

[mathwonk]

excellent free book:

http://www.math.miami.edu/~ec/book/

 

[JasonRox]

excellent free book:

http://www.math.miami.edu/~ec/book/

That is a good book too.

Every once in awhile I do a search, and this one seems to be one I bump into all the time.

 

[DeadWolfe]

The book I found easiest to understand (while still being comprehensive) was Birkoff & Maclane's Modern Algebra

 

[radou]

Just found https://www.amazon.com/dp/0486688887/?tag=pfamazon01-20 book on Amazon.com, seems like a good offer, anyone read it?

 

[mathwonk]

Now I have taught from Dummitt and Foote, and I no longer like it.

I recommend the books i listed above and my own web notes as better overall. Still there are some things in DF that are nice and not in my notes.best rec: Michael Artin, Algebra; and Van der Waerden, Modern Algebra; and Lang, Algebra.

and Hoffman- Kunze for Linear Algebra.

I also like my own notes but thnere is little data on them from other people.

 

[ircdan]

I will second Van Der Waerden! I have volume II and while I haven't read much of it, it's a great reference. The few proofs I've looked up are very well written and easy to follow.

Another good book is Jacobson's Lectures in Abstract Algebra. I've only read 1 section of Volume I and but it was very readable, and the proofs were really elegant! And again, the proofs are very clear and easy to follow.

Another good and fun to read book is Fraleigh. It's has 49 chapters so you feel like your making progress because the chapters are so small.

Rotman's Advanced Modern Algebra is also a good book. I've read 8 sections out of this and I find it much easier to read than DF.
I also think Rotman is a better reference than DnF, whenever I run into something I don't know, I usually have an easier time finding it in Rotman than in DnF.

Anyways since I've only used Van Der Waerdan and Jacobson as references, my recommendation is
Fraleigh (has less material, but easier to read)
Rotman's Advanced Modern Algebra (has way more material, a little harder to read, but easier than DnF)

Or maybe you should try Artin as others have suggested, I've never looked at it unfortunately.

Hope this helps!

 

[radou]

mathwonk (or anybody else), what do you make of https://www.amazon.com/dp/0387905189/?tag=pfamazon01-20? The reviews "sound" good, and I have found it to be in the top of the reference lists of some abstract algebra courses. The price is reasonable, too.

Although, in the end, I believe all of these books are respectable pieces of literature, it's only about one's individual interest and will to "do the math".

 

[ircdan]

mathwonk (or anybody else), what do you make of https://www.amazon.com/dp/0387905189/?tag=pfamazon01-20? The reviews "sound" good, and I have found it to be in the top of the reference lists of some abstract algebra courses. The price is reasonable, too.

Although, in the end, I believe all of these books are respectable pieces of literature, it's only about one's individual interest and will to "do the math".

It is a very well organized book. When Hungerford uses a result in a proof he always points you explicitly to where the result is found. Another interesting feature is that you can skip all propositions(and there lemma's and corollaries) without any loss of continuity. The proofs are for the most part, easy to understand.

I don't know if this is a good book to use for an introduction, it certainly is not as easy to read as other books that were mentioned in this thread like fraleigh, but then again, Hungerford, along with DnF, rotman, lang, etc are on an entirely different level because they are written for different audiences.

Note that I've only read about half of chapter 8, hence my comments on organization; i.e., I was able to jump into it and follow along since he cites what he is using in the proofs very well.
Hope this helps.

 

[Knavish]

Hi everyone,

My class is using Hungerford's undergraduate book ("Abstract Algebra: An Introduction"), I'm personally a bit vexed with it. So far, he has given no hint as to the historical development of concepts (i.e., the motives behind them), and furthermore, his proofs, to me, fail to outline the "big picture." I often end up nodding my head through each of the individual logical steps, but fail to grasp the proof as a whole--in a intuitive sense--unless I put in considerable effort of my own. I'm asking for your suggestions of books that will remedy these two issues.

As a note: I'm not a mathematics major. I'm looking for a better textbook because as long as I'm in this class, I might as well learn the subject properly.

 

[radou]

ircdan and Knavish, thanks for the comments. There are obviously always pros and cons about specific books.

I often end up nodding my head through each of the individual logical steps, but fail to grasp the proof as a whole--in a intuitive sense--unless I put in considerable effort of my own.

Sounds completely familiar - but in the end (as you mentioned), it's all about one's own efforts, which present a necessary condition to "do the math".

Anyway, I decided to order that book.

 

[Chris Hillman]

I'd second what the others say, that Hungerford is great as a reference, not so fun as a primary text as Michael Artin. Another valuable textbook is Jacobson, Basic Algebra (two volumes, drier than Artin but not as dry as Hungerford). The classic text by Birkhoff and Mac Lane is still an excellent choice for motivation and insight, not to mention the joy of reading a book written with style.

I'd add that one of the best short algebra textbook is Herstein, Basic Algebra. I happen to like Topics in Algebra for some things, but it seems mathwonk doesn't agree. But everyone seems to agree that Michael Artin's textbook is superb.

 

[radou]

I started reading/solving exercises from Hungerford about 2 weeks ago, and I'm very satisfied with the book for now.

If I keep my interest up, perhaps I'll give Artin a thought.

 

[thirdchildikari]

When I took a course in college last semester on group theory, the text we used was "Abstract Algebra -- A First Course" by Dan Saracino. I enjoyed it, and am planning on keeping the book around for reference/occasional messing around.

 

[teleport]

http://www.math.uiowa.edu/~goodman/algebrabook.dir/algebrabook.html

I found this wonderful thing the other day. I had started to look for something else since the book being used in my class is Undergraduate Algebra by Lang, which in my opinion is not enough for my class. The examples this book gives are just so trivial, when compared to the level of my class. I want to see examples of interesting symmetries, like symmetries of more complicated objects that are not the regular dihedral groups (not that they were given at all in the text), although yeah, they should be emphasized as well. There is not even an example of isomorphism map construction between any Zn type groups, and since they were not talked about, the exercises do not cover them. There is no motivation for the topics introduced, and just a complete lack of examples I need. Not for some strange reason the book is so small in size.

So I am reading this thread again. I seriously need another book, if I don't want to lose my interest. I am trying to find something with at least relevant examples like the ones mentioned. For my course, I don't need any linear algebra in it. I can't talk about the future topics of the course, but by what I've seen already, I can't trust my book.

 

[mathwonk]

well this browser just trashed another brilliant post.

basically go with books by the most eminent mathematicians, and among recent algebra authors that's artin.

 

[teleport]

Thanks. I'm just feeling a little scared of some of the reviews that I came across in Amazon for Artin's. I certainly do not need the linear algebra which some claim is quite abundant throughout the text. This would also be my first course in abstract algebra.

Chris mentioned Birkhoff and Mac Lane, which he states are high on motivation and "style". Seems interesting. What opinions would you have of these? Something that would probably thrill me is that one of these books covered algebra of n-gons and fun things like those which have always intrigued me. Man, wouldn't that be cool.

 

[teleport]

I will definitely go to the store. I'll take a look at these books, especially Artin's. Has anyone taken a look at the link? I can't stop reading that book. It talks about those symmetries which I have mentioned and way much more! It's just so beautifully written, with lots of graphics, motivation and style. I have read many theorems from that book already and the proofs seem clear. Could anyone tell me what they think of it? How in the world is it possible that such a high quality book comes free of charge? Man, you have to love the author!

 

[k3N70n]

I'm wondering why you (and maybe others) didn't like Gallians book. I'm studying it right now and I'm really enjoying it more than any other class I've taken. Maybe I just really like algebra but I a better text wouldn't hurt.

 

[annoymage]

i Google for Herstein "Topic in Algebra" and stumbled here, anyone have link to download the book in .pdf? i already have in .DjVu format, but I insist to have .pdf for some technical reason.