Is Dummit & Foote's Abstract Algebra the Ultimate Guide for Mathematicians?

[dijkarte]

A good book on Abstract Algebra that covers major undergraduate and graduate topics?
Something rigorous professional and for mathematicians.

Not Hungerford please, or any n x $100 book.

 

[lavinia]

A good book on Abstract Algebra that covers major undergraduate and graduate topics?
Something rigorous professional and for mathematicians.

Not Hungerford please, or any n x $100 book.

What do you want to learn and how abstract would you like the book to be?

Herstien's Topics in Algebra is a classic. You can get it used for $50.

Sah's Book is incredibly hard - but incredibly elegant.

But why not read a beginning book on Algebraic Geometry. You will have to learn a ton of algebra for this and a lot of abstract algebra comes form it.

You could also get a book on Algebraic Topology and learn algebra as you need it.

 

[SteveL27]

A good book on Abstract Algebra that covers major undergraduate and graduate topics?
Something rigorous professional and for mathematicians.

Not Hungerford please, or any n x $100 book.

Here are the ones I know about. Ideally one should read them all. Or maybe just read Disquisitiones Arithmeticae and try to figure out how Gauss did all that at age 21.

http://en.wikipedia.org/wiki/Disquisitiones_Arithmeticae

The classic algebra books.

* Van der Waerden
https://www.amazon.com/dp/0387974245/?tag=pfamazon01-20

This was the first "modern" algebra book that presented the subject as it's taught today: set theoretical preliminaries, groups, rings, and fields. Still an excellent book.

* Birkhoff - McLane
https://www.amazon.com/dp/1568810687/?tag=pfamazon01-20

A classical approach. Starts with a lot of material about concrete symmetry groups (reflections of the square, etc.) so that you really get a feel for what groups are about. Excellent book, not often mentioned these days.

* Herstein.
https://www.amazon.com/gp/product/0471010901/?tag=pfamazon01-20

This is a desert island book. It's a real classic. It's more modern than Birkhoff-MacLane but still classical in that it doesn't talk about category theory. This is arguably THE best undergrad abstract algebra book out there.

* Dummitt & Foote
https://www.amazon.com/dp/0471433349/?tag=pfamazon01-20

I'm not personally familiar with that one but it's pretty popular.

* Hungerford. Well you didn't want to hear about that. But if you're looking at grad-level texts, it's either Hungerford or ...

* Lang.
https://www.amazon.com/dp/038795385X/?tag=pfamazon01-20

Some call it comprehensive. Others call it incomprehensible. "Terse" and "austere" don't begin to describe it. As a book to learn from, personally I didn't like it. But as a reference, it's really good. There's a lot of material in there.

 

[dijkarte]

Yup these are options. After searching I've come across Elements of Modern Algebra by Gilbert, still cheaper than Hungerford's. I'm not sure about Dover stuff it looks dated...

 

[A. Bahat]

Don't forget Artin!

 

[dijkarte]

I'm now considering Dummitt & Foote based on the number of pages it has sounds comprehensive and covering a wider range of topics than others or maybe in more details...

Though Dover still tempting but not sure about quality of content, and I mean the material there is it reliable and advanced?