Book recommendation about Inverse Galois Theory
问题内容
I want to read about inverse Galois Theory with the goal of proving the Hilbert Irreducibility Theorem.
I do know the basics of Algebra (Group and Ring Theory, Field and Galois Theory, a bit of Moduls).
Is there any good book which is on an undergraduate level about Inverse Galois Theory?
回答 (1)
If your goal is Hilbert's Irreducibility Theorem, then I suggest
Field Arithmetic by Michael D. Fried and Moshe Jarden (Chapter 13)
Topics in Galois Theory by Jean-Pierre Serre
If you want an introduction to inverse Galois theory itself, then I suggest
- Inverse Galois Theory by Gunter Malle and B. Heinrich Matzat