I highly recommend 'A First Course in Abstract Algebra' by Fraleigh. We have used it the past year. This book does cover Galois theory. I have a unit on Galois theory next semester but we use a different text.
Hello Again!
I'm taking Abstract Algebra next semester, and I'm wondering if anyone [TPH, maybe?] can suggest any good books. This will be a two semester sequence for me, where I will learn about Field Theory, Rings, Groups, and all that fun stuff first semester. Then the second semester, I will be learning Galois Theory
I'd appreciate any book suggestions [on field, rings and group theory; or just Galois Theory], for I would like to get ahead in this class!!!
--Chris
By Abstract Algebra I assume you mean everything in general. As an introductory test you can use A First Course in Abstract Algebra. But do not plan on it being a serious book. That is because the more advanced sections of the book (like the more advanced section on group theory and Galois theory) are poorly written. You can get your self Beachy and Blair, which I like a lot more, to go further.
The Galois Theory in that book is a mess. .
It makes me feel sometimes that the author does not know what he is talking about.
Beachy and Blair do a good job on Galois theory.
I would recomment Field and Galois Theory by Morandi. That is a nice book.
But it is a GTM and immediately assumes a good knowledge of algebra.