66696 - Algebra Complements

Academic Year 2022/2023

  • Docente: Marta Morigi
  • Credits: 6
  • SSD: MAT/02
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Mathematics (cod. 8010)

Course contents

This course will be about Galois Theory, more precisely:

Splitting field of a polynomial. Symmetric functions. Normal fields extensions. Separable fields extensions. The primitive element theorem. Galois extensions. The Galois group of a field extension. The Galois correspondence. The Galois group of a polynomial. The discriminant of a polynomial. Cyclotomic extensions and radical extensions. Jordan Holder Theorem. Soluble groups. Solubility by radicals. Galois Theorem. Dedekind Theorem. Constructions with straight-edge and compass.

Readings/Bibliography

J.S. Milne "Fields and Galois Theory"

Cox "Galois Theory"

S. Lang, “Algebra”

S. Gabelli, "Teoria delle Equazioni e Teoria di Galois"

Assessment methods

Oral examination.

Office hours

See the website of Marta Morigi