Can someone please recommend a text on Galois Theory. Preferably not too heavy.?

Question

By not too heavy, I mean you don't need a doctorate in abstract algebra to be able to understand it.

Answer 1

Emil Artin was widely regarded as a great expositor, as well as one of founders of what is now modern algebra. His book "Galois Theory" is very small, begins with review of linear algebra and field theory before easing into the Galois theory, and is published by Dover, so it's cheap!

I am also fond of the first half of Irving Kaplansky's book, "Fields and Rings" -- the second half deals with noncommutative ring theory, but even covering both subjects, it is a pretty small book.

Answer 2

My two favorites are

Galois Theory by Joseph Rotman

and

Field and Galois Theory by Patrick Morandi

Rotman's book is a wonderful introduction to the subject which includes a nice appendix on group theory. It is the sort of book that can be used both as a serious study tool, and as bedtime reading. Morandi's book is more advanced and should be read after the basics of Galois theory are understood. It covers a great deal more material than Rotman and is an excellent reference for many important topics.

I like the above suggestion of Emil Artin's book, however it is a little misleading these days as his treatment does not use all of the same terminology and concepts used today. For instance, the notions of separable and normal extensions are not mentioned. As these are important concepts, you will need to read about them elsewhere.

The Dummit and Foote suggestion above should also be heeded as very few people come away from their book unhappy. Moreover, they use pictures in the Galois theory chapter; for how much more could you ask.

Answer 3

Asking for a text on Galois theory that is "not too heavy" is like asking for an easy explanation of particle physics.

In order to understand Galois theory you need to understand group theory and field theory. I studied Galois theory the last month of a year long graduate level Algebra sequence.

If you want the poor man's version, it goes like this.
In order to find the roots of certain equations, it is necessary to extend the rationals by adding irrationals. For example, you can't solve x^2 -2 = 0 in the rationals. But if you look at the field you get when you look at all number of the form a + b sqrt(2), you can find the roots. The field { a + b sqrt2} is an extension field.

When you study permutation groups that act on extention fields, you find that properties of the fields interact with properties of the groups. Galois theory is the study of those interactions.

Answer 4

These books are not solely devoted to Galois Theory, however I think that they approach the subject well.

Abstract Algebra by David S Dummit and Richard M Foote

Algebra by Larry C Grove

Answer 5

Galois Theory by Ian Stewart is a good text book.

Answer 6

Galois Theory by Ian Stewart. Depends what you mean by not too heavy, though. This is a nice book but is definitely mathematical.

Answer 7

Wikipedia entry http://en.wikipedia.org/wiki/Galois_theory seemed reasonably straight forward to follow

(I couldn't weigh it before posting but I don't think its that heavy :o) )

Answer 8

try google

Answer 9

LIVERPOOL ROCKS!!!!!!!