Title of the course: Field extensions and Galois theory
Instructor’s name: Prof. Luis Jaime Corredor
Institution: Universidad de los Andes
Dates: 21-27 July 2025
Prerequisites: Basic group theory (definition, subgroups, quotients, soluble groups). Basic ring theory (prime and maximal ideals, homomorphisms, quotients, definition of fields, divisibility in the polynomial ring K[x], K[x] is a principal ideal domain and a unique factorization domain).
Level: Advanced undergraduate
Abstract: We will study field extensions in general, and particularly the splitting field extension of a polynomial f(x) in K[x]. Then we will prove the Galois correspondence theorem that relates the structure of the lattice of intermediate extensions of the splitting field extension of a polynomial with the structure of the lattice of subgroups of ‘the Galois group’ of the polynomial, which is a finite group. We will present some applications of this.
Language: English
Textbook: D. J. H. Garling: A course in Galois theory.