Abstract Algebra Book: Find the Best Textbook for Rigorous Understanding

[HJ Farnsworth]

Hello,

A couple of years ago I studied abstract algebra from Dummit and Foote. However, I was never able to gain the intuition on the subject that I would like from that book. I want to study the subject again, and I want to use a different book this time around - one that covers a lot of ground, and gives rigorous definitions, but is otherwise fairly informal in its presentation.

I recently studied topology using Klaus Janich's "Topology" from the undergraduate texts in mathematics series. It was great, and I would like an abstract algebra equivalent to this book.

Does anyone know of an abstract algebra textbook that they would classify as being cut from the same cloth as Janich's "Topology"?

Thanks.

 

[micromass]

The book you should read is Armstrong's "Groups and Symmetry": https://www.amazon.com/dp/0387966757/?tag=pfamazon01-20
This is quite formal, but it gives a lot of intuition. It deals with group theory geometrically, which is the only way to really understand groups anyway. It only deals with groups though.

 

[HJ Farnsworth]

Cool, thanks. It looks like that the same series, so is probably the kind of thing that I'm looking for.

Anyone know any good ones to gain an intuitive understanding of other algebraic structures, e.g., rings, fields?

Thanks.

 

[verty]

Anyone know any good ones to gain an intuitive understanding of other algebraic structures, e.g., rings, fields?

Thanks.

There is one by Birkhoff & Mac Lane that looks good, the 3rd edition in print still.

 

[HJ Farnsworth]

That looks great. I think those two books should be just the combo I'm looking for.

Thanks very much.