Galois Theory books (in association with Abstract Algebra books)

Question

I know that there have been written similar posts, and I used them as a source for my question.

I ' m looking for a book for Galois Theory (Construction of fields. Algebraic extensions - Classical Greek problems: constructions with ruler and compass. Galois extensions - Applications: solvability of algebraic equations - The fundamental theorem of Algebra - Roots of unity - Finite fields), which has the following characteristics:

• Logical order in the presentation of the theorems, definitions and generally of all concepts.
• Thorough analysis of each proof, example etc.
• Many examples and good exercises to solve.
• Also, to be suitable for self-study and for the first touch in the subject.

I should notice that I don't like Stewart's and Rotman's book.

What's your opinion for 1) Galois Theory by Bakers, 2) Galois Theory by Roman, 3) Fields and Galois Theory by Howie, 4) Galois Theory by Jean-Pierre Escofier. And do you believe that it is better to read from a general Abstract Algebra book, such that Fraleigh's/ Dummit's and Foote's/Gallian's?

Thank you in advance.

Answer 1

I recommend Galois' Theory of Algebraic Equations, by Jean-Pierre Tignol (2nd edition, World Scientific, 2016).

Answer 2

You clearly know which books are available on the subject. I would like to comment on your request. "Also, to be suitable for self-study and for the first touch in the subject."

The lecture notes of Christopher Cooper on Galois Theory ( Math338 ) are just that: suitable for self-study, and for a first touch in the subject.

https://coopersnotes.net/third_galois.html

Answer 3

I’ve learned Galois Theory from Siegfried Bosch’s Book Algebra. It’s German, though. To my knowledge, it has been translated to English, but I do not know how available English versions are.

Anyway, it pretty much fits the bill: It is very clean, leaves absolutely nothing out (not even set-theoretical considerations when discussion transcendence degree), it is well-structured and yet light-to-read. And it covers, of course, everything you have listed.

It also has additional (starred) sections on more advanced topics. I most of all value his introductions to each chapter which motivate the following material really well and give a good overview of what to expect (which makes it really suitable for self-study). The introductory chapter also gives some historical context.