Algebra Textbook for Abstract Algebra / Group Theory

[BubblesAreUs]

I am looking for an accessible textbook in group theory. The idea here is to use it to learn basic group theory in order to take up Galois Theory.

My background includes Calculus I-IV, P/Differential Equations, Discrete Mathematics including some graph theory, Linear algebra, and am currently studying Complex Analysis, foundations of mathematics and analytic theory of differential equations. Unfortunately, I have yet to take up abstract algebra ( due to work commitments) despite taking a rigorous course in linear algebra so consider me a total noob.

Shall be awaiting for recommendations.

 

[The Bill]

I highly recommend A Book of Abstract Algebra by Pinter. It handles the same level of material as my undergraduate abstract algebra class did, and also includes Galois theory at the end. Also, it is written in a pleasant conversational style without sacrificing precision, coverage, or rigor.

 

[BubblesAreUs]

Thanks Bill.

Would you consider this textbook good as a standalone text? If so, which chapters would you recommend going through in order to learn Galois Theory. I alreadyknow that a semester course in abstract algebra is not required even though I'm planning to take it next semester.

 

[The Bill]

It could have served just fine as a standalone text for the course in abstract algebra I took as an undergraduate. The main point there is that it has good exercises and explains what is needed for those exercises in the text.

I'd say you should probably work through all the chapters on group theory before going to the chapters on Galois theory. So work through, say, at least the first sixteen chapters then skip to chapters 31-33. You might still want to cover some of the applications and other algebra topics in the intervening chapters, but by the time you get to chapter 16, you should have a better idea of what you want to cover.

 

[BubblesAreUs]

Another question. How does the text define a ring with respect to multiplicative inverses?

 

[The Bill]

The definition of a ring in the text doesn't require a ring to have a multiplicative unity or inverses. Pinter uses the term "ring with unity" to denote a ring with a multiplicative unity. He then goes on to discuss such rings, explaining the possibility of some elements being invertible, etc.

 

[BubblesAreUs]

Excellent. I can't wait till I get my hand on this text.

Thanks, once again.

 

[mathwonk]

when i taught algebra in college for years we never got to galois theory, because it was the last topic. so one year i decided to do it first so i coulod learn it. it turned out that is not possibloe because galois theory uses grouop theory, ring theory, and a little linear algebra. but i did do just enough of each of those to be able to do galois theory as soon as possible. and i wrote up the niotes for the cousre and out them on ym webpage for free download, the subject com0ruses the contents of the first 4 parts of the grad algebra course, namely 843-1, 843-1, 844-1, and 844-2. you are welcome to them, but of course they may not be as good as what you have. stll they are free, and several of my students did become math phd's, and used them to pass prelims etc...

http://alpha.math.uga.edu/~roy/one outstanding source for galois theory is the old harvard notes by that name, written by the great richard brauer in 1957-58, revised 1963-64. i don't know where you can find those except maybe in a good math library...well there is a used copy listed on amazon for over $700. it is worth maybe $25. how do these people sleep at night?